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Whose idea of Simultaneity is Wrong?

Two inertial observers in motion relative to one another may disagree as to which of two events happened before the other.

They are both drawing reasonably sensible and natural conclusions from their respective observations – assigning what they actually see to a time that is earlier by the light travel time (which they compute from the observed distance and the measured speed of light). But since they disagree one or both must be wrong if they both think their own idea of simultaneity is the only “right” one.

It could be that one of them (or perhaps some other inertial frame) is “right” in some sense and all the rest are “wrong”. But we don’t have any way of exactly identifying the “right” frame, and using that fact as a starting point provides a way of making accurate predictions without needing to make the untestable assumption that some arbitrarily chosen particular frame is in fact the special one.

Source: (1000) Alan Cooper’s answer to In twin paradox, the traveller’s clock ends up with a lesser total elapsed time, so we can tell who made the trip. Does this not contradict the postulate of SR that all physical laws are the same in all frames and all inertial frames are equivalent? – Quora

Where in the universe can we find such an inertial frame? Certainly not on the surface of earth!

SR only applies exactly in the absence of gravity. So in the real world it is just an approximation that works well enough for predicting things where the effect of gravity is small (such as interactions between small high velocity particles in accelerators near the Earth’s surface, or between spacecraft and small bodies like asteroids far from planets, but not for things like apples falling out of trees on Earth).
In regions where it does provide a good approximation, it works just as well for accelerated as unaccelerated frames, but for accelerated frames the formulas needed to express physical laws in terms of the observer’s coordinates are more complicated.

Source: (1000) Alan Cooper’s answer to In twin paradox, the traveller’s clock ends up with a lesser total elapsed time, so we can tell who made the trip. Does this not contradict the postulate of SR that all physical laws are the same in all frames and all inertial frames are equivalent? – Quora

So the excuse used NOT to apply relativity theory in the twin paradox is a brief period of zero seconds at the turnaround point?

No one who knows what they are talking about has suggested “NOT to apply relativity theory”. On the contrary, the correct application of relativity theory leads to the conclusion that when the twins re-unite they agree on the fact that they have both seen the traveller age less. They just disagree on when during the trip the Earth-based twin aged faster. The one on Earth thinks it happened at a steady rate throughout the trip and the traveller (after actually seeing it during the return trip) thinks (after making the light travel time correction) that it happened quickly during the turn-around.

Prior to the turn around, each sees the other ageing more slowly (due to the Doppler effect) and, even after making the light travel time correction, thinks that part of that slowdown remains unexplained (and so in some sense is “really” happening).

But any claim that during the outbound journey “we know for a fact that the travelling twin is younger than the earth twin” (or vice versa) is completely false. There is nothing that is absolutely true about the relative ages of the twins until they are at rest with respect to one another.

Source: (1000) Alan Cooper’s answer to In twin paradox, the traveller’s clock ends up with a lesser total elapsed time, so we can tell who made the trip. Does this not contradict the postulate of SR that all physical laws are the same in all frames and all inertial frames are equivalent? – Quora

More on “Collapse”

The “state” of a system that is studied in quantum mechanics is not a property just of the system itself, but rather it is a summary of what is “known” about that system by a class of outside “observers” who do not interact with it in any way between “observations”. (The “observers” don’t actually have to be conscious; anything such as a measurement apparatus that could be changed in some macroscopic way by interaction with the system could play the same role, with the relevant change being identified as “knowledge” so long as different macroscopic states of the “observer” end up associated with different values of whatever property is being “observed”.)

This relative state changes whenever the observer learns something about the system – and when that happens the probabilities of all values other than the one observed become zero (while the value experienced by the observer becomes certain from the observer’s point of view). This change is sometimes called “collapse” – though it should be noted that the total of all the probabilities remains the same, so it might be better to think of the probability distribution being collapsed “sideways” onto the observed value rather than “down” to zero everywhere.

As an example, consider the case of an electron that has just passed through a selector that ensures that its spin in the z-direction is positive (let’s call this “up”). If we think of the spin of the electron as a system in its own right and if we can control the path of the electron without interacting with its spin, then we can represent (what we know about) the spin by a quantum state, and it turns out that if we know the spin is up then we cannot assign any particular value (say left or right) to any horizontal component. All we can say is that if we pass many such electrons through another vertical spin selector they will all measure spin up, but if we measure in any horizontal direction we’ll get positive and negative results with probability 1/2 each. BUT (and here’s the “collapse”) if, on doing that horizontal measurement, we observe spin (say) left, then when we subsequently measure the same horizontal spin we’ll get the same result with certainty and the probability of seeing right will have gone down to zero (while if we go back to measuring the vertical component it will now have equal chances of being up or down – which is another reason for not liking the “collapse” language since what collapses one distribution has spread out another, and in particular has raised the chance of seeing down next time from 0 to 1/2).

Note: Jonathan Joss makes a similar objection to the word “collapse” and suggests that it be called a “rotation” of the state vector (but of course in the relevant Hilbert space rather than physical space).

Source: (1001) Alan Cooper’s answer to Can you give some examples where an object’s state changes due to its being observed by an outside observer (observation collapsing wave functions)? – Quora

Dead or Alive?

All I know for sure is that any cat whose owner would subject it to such an experiment cannot have been “Wanted”.

But if Schrodinger had had many cats to try this on I guess about half of them would be dead and the other half alive. And in all cases the “collapse” would have occurred long before the box was opened – or rather never, because a cat could never be put into a pure quantum state in the first place.

Source: (1001) Alan Cooper’s answer to After Schrodinger opened the box with the cat inside, and thoroughly observed the cat, collapsing the superposition, was it dead or alive? – Quora

(1001) Alan Cooper’s answer to Can you give some examples where an object’s state changes due to its being observed by an outside observer (observation collapsing wave functions)? – Quora

The “state” of a system that is studied in quantum mechanics is not a property just of the system itself but rather is just a summary of what is “known” about it by a class of outside “observers” which do not interact with it in any way between “observations”. (The “observers” don’t actually have to be conscious; anything such as a measurement apparatus that could be changed in some macroscopic way by interaction with the system could play the same role, with the relevant change being identified as “knowledge” so long as different macroscopic states of the “observer” end up associated with different values of whatever property is being “observed”.)

This relative state changes whenever the observer learns something about the system – and since since this results in the probabilities of all values other than the one observed becoming zero (while the one experienced by the observer becomes certain from the observer’s point of view) it is sometimes called “collapse” – though it should be noted that the total of all the probabilities remains the same, so it might be better to think of the probability distribution being collapsed “sideways” onto the observed value rather than “down” to zero everywhere.

As an example, consider the case of an electron that has just passed through a selector that ensures that its spin in the z-direction is positive (let’s call this “up”). If we think of the spin of the electron as a system in its own right and if we can control the path of the electron without interacting with its spin, then we can represent (what we know about) the spin by a quantum state, and it turns out that if we know the spin is up then we cannot assign any particular value (say left or right) to any horizontal component. All we can say is that if we pass many such electrons through another vertical spin selector they will all measure spin up, but if we measure in any horizontal direction we’ll get positive and negative results with probability 1/2 each. BUT (and here’s the “collapse”) if, on doing that horizontal measurement, we observe spin (say) left, then when we subsequently measure the same horizontal spin we’ll get the same result with certainty and the probability of seeing right will have gone down to zero (while if we go back to measuring the vertical component it will now have equal chances of being up or down – which is another reason for not liking the “collapse” language since what collapses one distribution has spread out another, and in particular has raised the chance of seeing down next time from 0 to 1/2).

Note: Jonathan Joss makes a similar objection to the word “collapse” and suggests that it be called a “rotation” of the state vector (but of course in the relevant Hilbert space rather than physical space).

Source: (1001) Alan Cooper’s answer to Can you give some examples where an object’s state changes due to its being observed by an outside observer (observation collapsing wave functions)? – Quora

(1001) Alan Cooper’s answer to Why does the twin paradox assume the “stationary” twin will become older than the “moving” twin due to time dilation? There are no absolute speeds, speed is relative, and either twin could be considered to be moving at close to the speed of light. – Quora

Yes, it is true that “either twin could be considered to be moving at close to the speed of light”. And it is also true that so long as neither of them accelerates each will think that the other is ageing more slowly. But this is no paradox as there is no way for them to get together to see who is right. That can only happen if one or other of them turns around. And in that case whoever turns back towards the other will end up thinking that the other aged so much more quickly during the turn-around that when they get back together there will be a well-defined answer to the question of who is indeed younger and by how much. (They will not agree on the exact pattern of “when” the different ageing rates occurred, but since there is no absolute definition of “when” for events that do not happen at the same place, that disagreement is just a matter of having different points of view.)

Source: (1001) Alan Cooper’s answer to Why does the twin paradox assume the “stationary” twin will become older than the “moving” twin due to time dilation? There are no absolute speeds, speed is relative, and either twin could be considered to be moving at close to the speed of light. – Quora

Moving Through Time

Time does not even exist without some frame of reference, as space and time are just ways of assigning coordinates to events and different observers may do so in different ways. And in terms of any particular frame of reference, motion through space is usually thought of as having different positions at different points in time. Since the position varies with the time I suppose this could be described by saying that we “move with time”. But the idea of motion through time is kind of vacuous since any choice of time coordinate obviously changes when it changes; so I guess we could always be described as moving with time through the same time at “speed” one. This might get more interesting for the case of different reference frames with different time coordinates – in which case one might be moving with the time of one frame through the time of another (with a rate that would correspond to the Lorentz time dilation factor corresponding to the relative speed between the two frames).

So whether you are moving through space or time depends on what coordinate system you are using. In terms of coordinates based on your own body you are always fixed in space and “move” only through time. But in terms of the coordinates of a frame that is moving with respect to you, you are moving through its version of space (with exactly the opposite velocity).

Source: Alan Cooper’s answer to If space and time are related, how can someone move through time without moving through space (sitting still)? – Quora

and https://www.quora.com/Do-we-and-probably-everything-else-move-through-time-or-do-we-move-with-time/answer/Alan-Cooper-5

Michael Price’s answer to How does the Many Worlds Interpretation of Quantum Mechanics explain the emergence of probabilities according to the Born rule? – Quora

Source: (1001) Michael Price’s answer to How does the Many Worlds Interpretation of Quantum Mechanics explain the emergence of probabilities according to the Born rule? – Quora