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12

Dear Jack, there is no physical phenomenon that could be called the collapse. The collapse of the wave function, as first emphasized by Werner Heisenberg and then many others, is just the event when we learn something about a physical property of a physical system. When we learn that Osama bin Laden is located in a building in Pakistan, his wave function - ...


11

Hannesh, you are correct that the second law of thermodynamics only describes what is most likely to happen in macroscopic systems, rather than what has to happen. It is true that a system may spontaneously decrease its entropy over some time period, with a small but non-zero probability. However, the probability of this happening over and over again tends ...


8

There are currently two different accounts that give a larger picture of what happens when a quantum system is measured. One of them is the fact that many random interactions between the system (which might be a 1-body or N-body quantum system) and the environment (which is considered for most purposes a pseudo-classical system with infinite degrees of ...


6

The laws of physics are time reversible, so a clock could tick backwards as well as forwards. However in our current low entropy universe it is vastly more probable that the clock ticks forwards. In a maximum entropy universe the probablility of a backwards tick would be identical to a forwards tick, so on average the clock time wouldn't change.


5

The summing over final states and the averaging over initial states is a good observation that I always emphasize as the origin of the arrow of time. As soon as one considers mathematical logic, this asymmetry has to arise. Why are we summing over final states? Because "we don't care" about which of them occurs (and no one knows). We're calculating the ...


5

We do all the "cross section business" because we want to predict results of experiments. Let's take for example some particle with two polarizations states: "+" and "-". You know that experimentalists will collide 1 000 000 pairs of particles, with polarisation of initial particles being unknown. Best thing you can do is to hope that in experiment ...


5

You ask: From my studies in quantum mechanics, I don't remember any postulates stating anything like this, but this all makes sense to me. Are there any theories out there that go along these lines? Indeed there is such a theory. It's called decoherence. You mention the comparison with thermodynamics, and this is basically the same way decoherence ...


5

The microscopic laws of physics are reversible or, to say the least, CPT-symmetric (processes are invariant if they're run backwards in time, in mirror, and with antiparticles). The CPT symmetry follows from the Lorentz symmetry. Langton's ant as well as pretty much any other Turing machine or cellular automaton fails to be microscopically reversible; ...


4

Just a few pointers for you to explore more on this. Check out Aharonov's paper the time symmetric formulation of quantum mechanics: http://arxiv.org/abs/quant-ph/9501011 Tony Leggett talks about this: http://www.youtube.com/watch?v=IGim9uzcumk It's a nice video and quite simple to understand.


4

I'm not sure if there's a definitive answer because I've seen it discussed recently at high level. I do think there's some broad agreement that entropy is important because it has an irreversible property: closed systems progress from low entropy states to higher entropy states. So we can define the passage of time more precisely by talking about increasing ...


4

Time seems to "pass" because it is not symmetric -- it is T symmetric. This is often called the "arrow of time." The arrow of time points in the direction of increasing entropy. More: http://en.wikipedia.org/wiki/Arrow_of_time The real question you are asking is why our minds perceive this direction...


4

First of all, it's strange how the OP jumps from the Loschmidt "paradox" to dissipation. It makes it very unclear what he or she is actually asking because dissipation has no direct relationship to the Loschmidt "paradox" except that both of them are issues concerned with irreversibility in statistical physics or thermodynamics. The existence of dissipation ...


4

Loschmidt's paradox is that the laws of thermodynamics are time asymmetric because entropy always increases, but the underlying laws of physics are symmetric under time reversal. It should not therefore be possible to derive the second law of thermodynamics from first principles. Opinions in the scientific community differ as to whether this has been ...


4

A scalar with a unit is a 1-dimensional (axial) vector; changing the basis corresponds to changing the unit. A number (without a unit) is not a 1-dimensional vector in the terminology used by physicists. However, it is a 1-dimensional vector in the terminology used in linear algebra.


4

I suppose that what you are thinking about is the principle of causality. We have two events: a cause and an effect, where the second event is a consequence of the first. That is how we perceive all events around us and what we intuitively accept as true. In physics, however, we sometimes obtain two different solutions: first with the cause before the ...


4

By increasing the precision of the measuring instrument AND making the measurement, the observer CAN decrease the entropy of the observed system (by redefining what is macro-state). But the total entropy of the observed system plus the observer will increase. This is because every act of measuring increases entropy of the entire system. In other words, it ...


3

An often good on-line source for the interpretation of quantum theory is the Stanford Encyclopedia of Philosophy, which has a page on "collapse theories". There is a lot of literature on whether one needs collapse if one takes the wave function seriously, as opposed to the mainline Physicist's approach of taking a more empiricist view, as outlined well by ...


3

The statements of the age of the universe timescale are related to the cosmic time, a timescale derived from the expansion of the universe in general relativity of a roughly homogenous universe (the Friedmann-Lemaitre universe/metric). Different homogenous densities of the universe define different cosmic times. The assumption is a homogenous ...


3

A vector in a $1D$ space is not a scalar. But if we choose a basis (which in this case consists only in one vector, say $E$), any other vector is of the form $vE$, with $v$ a scalar. So we can identify the $1D$ vector space with $\mathbb R$, but the identification depends on the choice of $E$. In the case of the time, things are similar. For the Minkowski ...


3

You seem keen to exclude the thermodynamic arrow of time, but as far as I know that is the only source of time asymmetry. As Ross mentioned in his answer, the collapse of the wavefunction has been presented as a time asymmetric process. However I would guess most people now view even this as fundamentally time symmetric. If you believe in decoherence the ...


3

Actually, it's not true that our laws of physics are symmetric under time reversal. The Standard Model of particle physics isn't. In fact, it's been strongly suspected since the 1960s that the laws of physics can't be invariant under the operation of time reversal. There is a very reliable theoretical result called the CPT theorem which says that any ...


3

Your example is an example of a microstate in your sample, which is a statistical ensemble and its entropy is defined by the number of microstates possible. Where S is the entropy and K is the Boltzman constant and Ω is the total number of microstates. One of these microstates you show contributes to the Ω as one state. It will immediately flow into ...


3

The molecules can assemble in one corner of the room. The point is that it's exceedingly unlikely to happen. It is so unlikely in fact, you will to best approximation never see it happening that all air molecules spontaneously assemble in the corner of a room even though it isn't forbidden by the laws of physics. But if you wait long enough, it will happen ...


3

People defined time as a variable going forward long before entropy was defined. Biological/consciousness time, which you also discuss, forced the concept of time and a way /unit to measure it, as cultivation and buildings forced a concept of space and units to measure it. The celestial clock of sun moon and planets was used even by primitive people. ...


2

Contrary to the general tone of the answers I have read so far, I feel there are indeed real difficulties in quantum mechanics which fall under the general category of "collapse of the wave function". I think part of the problem is the tendency of people to talk in generalities instead of dealing with specific issues. I am therefore going to list a few of ...


2

I think most people would say the paradox is resolved - but, as the answers to this question make clear, they wouldn't necessarily agree about who resolved it or what precisely the resolution is. For my money the paradox was elegantly resolved by Edwin Jaynes in this 1965 paper. In Jaynes' argument, the symmetry is broken by the fact that we, as ...


2

You mention the expansion of the universe, so I'm assuming your question is in the context of General Relativity. The first thing to make clear is that the expansion of the universe is an expansion in spacetime and not just an expansion in space. We see it as an expansion in space because we are comoving observers, but this is an accident of the co-ordinate ...


2

|Dear Mr Student, the time-reversal symmetry in conventional QM at best (e.g. no magnetic fields) only applies to the unitary evolution of a quantum system; the measurement process is not time-reversal symmetric. Also, the second law of Thermodynamics says (very roughly speaking) the Entropy should decrease if you go back in time; again there is no ...


2

If I'm reading your question correctly, it is at least in part whether the nominal event of "wave collapse" (please note that different schools of thought describe that event differently!) is reversible in time. I won't try to address the schools, but rather whether what you ask has any experimental meaning. This is not a complete answer, but the concept of ...



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