23

Yes, it would travel further than $0.99c \times 2.2 \,\mu\text{s} $. It would travel $\beta \gamma c \times \Delta t$ because of time dilation. This does not mean however, that the muon or the bomb see the surroundings moving faster than the speed of light. This is because in the frame of the muon distances are relativistically contracted. So if you have ...


17

The measurement problem is one of the most relevant open problems of quantum mechanics. What is a measurement? What constitutes an observer and what doesn't? Is the wavefunction a physical object (ontological) or just a mathematical construct that represents our ignorance of the state of a system? Trying to answer these questions has produced a multitude of ...


11

Time dilation goes along with length contraction. Consider a muon that we measure travelling at 50 km when it "should" have only travelled 600 m. We say it travelled 50 km because we have conventional reference frames that are convenient for us to use that say that distance is 50 km. The muon, however, is moving a substantial fraction of the speed ...


4

You did not explicitly state it, but I assume that you also intend the material of the box to be very rigid such that when the pressure increases inside the resulting increased stress does not produce any measurable increased strain. I.e. the size of the box is unchanged before and after. This scenario is well studied in the literature for a spherical box. ...


4

Informally, one major conclusion of special relativity is relativity of simultaneity. Two events that are seen (or can be deduced as) simultaneous by one person, will not necessarily be simultaneous to a moving observer. But let me try to illustrate what that really means. What happens is that their space and time coordinate axes reorient in a particular way....


4

The principle means that it does not matter which observer accelerated beforehand, or indeed, whether they both did- once they are in inertial motion relative to each other, either can be taken to be at rest. More generally, you should not imagine that the rules of SR require observers and clocks. Instead you should consider it a more general and abstract ...


4

It's unclear when, or if, wave function collapse happens. What is clear is that everyone agrees in principle on what measurements occur and what their outcomes are. The only situations I can think of that resemble "observer-dependent measurements" are: In the many-worlds picture, generally different measurements occur in different worlds (and of ...


3

Your frame of reference, i.e. the car is accelerating. So it is not an inertial frame of reference. If you were travelling with constant velocity, then both the observers and your interpretation would be equivalent. But you are accelerating. And you can feel the effects of that acceleration as you feel a pseudo force pushing you backwards when you hit the ...


3

"Why are there different formulas because isn't movement relative, and it shouldn't matter whether the source or the observer is moving?" Your reasoning applies to light but not to sound. This is because, in the case of sound, there is a third thing involved: the medium. It isn't just a case of source and observer. To understand this properly there'...


2

I think it's best to answer this question first in the context of classical field theory. In classical field theory on curved spacetimes, we don't usually consider field equations and observables which single out a preferred reference frame. (You can do this, but it's not very useful for doing gravity or electromagnetism.) But it does (frequently) happen ...


2

Does that mean that from the crew's time dilated perspective, they would experience less acceleration than we observe in our frame of reference? No, the crew’s proper acceleration (the acceleration they feel) is greater than the coordinate acceleration (the derivative of their velocity in our frame) that we observe. They can continue at 1 g proper ...


2

I would suggest that collapse of the wavefunction is a useful approximation, not a mathematical absolute. Prallax has given a good summary of the positions. Under this view, a big thing (in the Copenhagen interpretation) is big enough that you will never see superposition effects. The distinction between big and small is not sharp, it is dependent upon ...


2

There is no such thing as wave function collapse. If there were, the Schrödinger equation would be wrong. Measurement requires a measurement apparatus with multiple orthogonal states. Each of these states is entangled with part of the wave function of the system to be measured. These parts are what you could call collapsed wave functions. They are collapsed ...


2

When we say that a quantum mechanical object, such as a particle, is subjected to a measurement, we mean that it is interacting in some way with other particles, namely those that form the measuring device. To ascribe some special quality to a measurement, as opposed to any other form of interaction between particles, seems obvious nonsense. Particles ...


1

My assumption for this answer is that the front of Alice's rocket passes by the front of Bob's rocket at the moment Bob's clocks all read $0$. In Alice's frame, we can define the event coordinates for Alice's clocks as $(c(0),-90),(c(0),-45),(c(0),0)$. Let the coordinates for the same events in Bob's frame be $(ct_1, x_1), (ct_2,x_2), (ct_3,x_3)$ ...


1

If the source is moving directly away from the receiver (i.e. on the line connecting the source and receiver), then you are right. The observed frequency at the receiver is constant as long as the frequency and velocity of the source is constant in that case. The issue is when the source moves along a line that does not contain the receiver, e.g. like a ...


1

Wave collapse is to a large extent a matter of interpretation. In MWI, there is no wave function collapse. Rather, the observer becomes entangled with the state, and the combined system has a component in which the observer sees one result, and other components where the observer sees other results. In the Copenhagen Interpretation, "observation" ...


1

If a ship starts from rest in a frame S, $a'$, the acceleration in the rest frame, S', of the crew is related to the acceleration, $a$, in S, by $a'=\gamma^3 a$.


1

There is no frame of reference in SR in which an acceleration can stay constant at a non zero value for an infinite amount of time. This would inevitably lead to a velocity that is greater than the speed of light. It is well-known that when two frames $S$ and $S'$ move relative to each other with velocity $v$ and a velocity is $w$ in $S$ then in $S'$ it is $$...


1

would it travel further than (.99c x 2.2 microseconds)? If you send it out at a velocity, relative to Earth, of .99c, then Earth's spatial component (that is, the spatial component in Earth's reference frame) of the displacement between it being sent out and its exploding is more that .99c * 2.2 microseconds. The bomb's spatial component of the displacement ...


1

Can we prove that the hypersurface of $\Sigma_t$ is the surface of the events that happen at the same proper time of an Eulerian Observer/ ZAMO at $\infty$? It is extremely common for people to pick a coordinate system, show that at $r=\infty$ their $t$-coordinate (say) coincides with proper time for a given observer, then conclude the $t = \textrm{const}$ ...


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