JonG

[i} So the particles are not in a known state before the measurement, they are in a superposition.[/i] This is not what is being suggested. Whichever view is taken, the state of the system would be unknown before measurement. In fact, it's hard to see how these different ways of looking at the experiments could differ in their predicted outcomes. According to one view, the act of measurement causes a wavefunction to collapse into a single state and what is observed corresponds to that state. According to the other, the system is in that entangled state before the measurement was made and wavefunction collapse doesn't occur. In both cases, the states would be entangled but there is no way of predicting what the state is going to be before the measurement is made. Whichever way one looks at it, the state of the system when a measurement is made would be of the same degree of uncertainty - it's a question of how did it get into that state rather than what the state is. My interest in this really is to do with the idea of collapse of a wavefunction. As suggested by the authors referred to earlier, this postulated collapse is a process about which we know almost nothing and, in the case of entanglement, it leads to the conclusion that information about the state of the system is transmitted between spatially separated points instantly. This latter problem would not arise if the system was assumed to be in the state it was found to be in before the measurement was made. Oddly, some entanglement experiments actually cast doubt on the collapsing wavefunction explanation. I believe that Alain Aspects experiment using photons established that there could be no causal link between the measurements on different photons, and yet the wavefunction collapse explanation suggests that one measurement initiates the collapse of the wavefunction which then determines the outcome of the other experiment!

What do you mean by the system is in a single state? Because entangled particles can be thought of as being in a single state. Yes, they would be in the single state - the one on which measurements were made. But the usual contention is that, before measurement, the state of the particles is represented by a linear superposition of eigenstates which collapses into a single state when a measurement is made. In a larger picture, I'm not sure the article is arguing about what you are asking. I don't see the relationship between entanglement and whether wave functions are "real" (and I don't see much in the way of clarification of what they mean by "real") The article (I refer to their published paper) is not specifically about entanglement but it does make the statement: "If a quantum state is a physical property of a system then quantum collapse must correspond to a - problematic and poorly defined - physical process." In the article, they advocate that the quantum state is a physical property of the system and this implies that the process of "collapse" is as they put it, problematic and poorly defined. However, collapse into a single state appears to be the "process" usually invoked to explain why measurements on entangled particles correspond to each other. (As far as I am aware, nothing is known about this collapsing process - it is simply postulated). So I think that their views have some relevance to the usual accounts of entanglement. Relevant quotes referring to what is written above: "Many others have suggested that the quantum state is something less than real. In particular, it is often argued that the quantum state does not correspond directly to reality, but represents an experimenter's knowledge or information about some aspect of reality. This view is motivated by, amongst other things, the collapse of the quantum state on measurement." Their distinction between real and unreal amounts to whether or not the regions of phase space corresponding to the descriptions of the system in different states overlap or don't overlap. However, it's necessary to read through the article to see that - they are not using term "real" in some casual way. Briefly, they give examples along the lines of: - If a system with a property which has the value P occupies a region of phase space, and this region overlaps with one corresponding to the property having the different value P', then this property can't be real because in the region of overlap it would have two different values.

(It is times like this I wish I had the expertise to really understand what they are doing!) I know exactly what you mean. There are times when I fee that if I were to delve into everything that I find puzzling on page 1, I would never get to page 2 !

Isn't that what is described as a hidden variable in Bell's Theorem? The hidden variable notion arose with Einstein who appears to have believed at some point that something was missing from quantum theory. However, the Pusey at al suggestion doesn't require anything to be missing from quantum theory - it seems to be more matter of how one interprets the idea of a wavefunction. I have to admit that this area is littered with terms like "hidden variable" to the extent that one is unsure what is being referred to. Also, the precise meaning of "objective underlying physical state" is not clear. (I don't know how well the Pusey et all suggestions stand up to close scrutiny in accordance with Bell's inequalities but it isn't obvious that they would be relevant.)

"Sounds like you are looking for Bell's Theorem: http://drchinese.com...m_Easy_Math.htm" Bell's inequalites are clearly related to the interpretion of entanglement experiments, but I am not sure that they relate to the suggestion put forward by Pusey at al. The essential difference seems to be whether a system is in a particular quantum state prior to measurement or whether the act of measurement put it into that state. I don't think that the Pusey et al suggestions involve things like "hidden variables" that are often mentioned in this context.

"If the system was in a single state beforehand, then you would get different results from what we see in some experiments." I don't understand why the results would be different. If the single state were to be the same as that which the wavefunction is assumed to collapse into, why would the results of a measurement be different? I would be grateful if you could indicate which experiments can only be explained on the basis of a collapsing wavefunction.

The phenomenon of quantum entanglement appears to rely upon the belief that prior to measurement, a system is represented by a linear combination of eigenstates but that, when the measurement is made, its wavefunction collapses into a single state (which one isn't known beforehand) which is shared by the whole system. If the system was instead in a single state before measurement, any measurement, regardless of where it was made, would give a result consistent with that state and the mystery of entanglement wouldn't arise. What I am trying to do is to decide whether the above presumption is what is implied by the paper published by Pusey, Barrett and Rudolph and described here: http://phys.org/news/2012-05-paper-controversy-nature-quantum-function.html

Actually, there is a very cool reason as to why a heat engine could be 100% efficient. All you have to do is to ensure that the low temperature side is at absolute zero which, unfortunately, can't be done. It reminds me of a restatement of the laws of thermodynamics which I once heard from someone who specialised in the area. 1st Law: You can't win, you can only break even. 2nd Law: You can only break even at absolute zero. 3rd Law: You can't get to absolute zero.

Apologies in advance for being a little off-topic, but I read recently in a book by G.J.Whitrow that the ancient Greek mathematicians didn't get round to a clear definition of speed. The reason given was they regarded a fraction as the ratio of the size of one thing to another thing of the same type, so that they could divide a length by a length, for example, but not a length by a time. It this is true, it seems odd that people who were so adept at geometry were so awkward when it came to algebraic matters.

Just in case it has't already been mentioned, the kilowatt hour (kWh) is a unit of energy. In my case, the conversion from volume of gas used to kWh is given on my gas bill, for example; "Units used = 20 m3, kilowatt hours = 219" I have a smart meter and cubic feet don't appear anywhere on it. If I do read it, the reading is in m3.

Regarding the above statement, the speed at which the earth is moving wouldn't have any effect on the reading from the speedometer. For time dilation to be observed, two frames of reference moving at different speeds are required, and what is being observed should be an interval in time. As already mentioned, one frame of reference could be the frame of reference of the car, and another could could that of someone standing on the ground watching the car go by. These frames of reference would be moving relative to each other. The time interval could, for example, be the time it takes for the driver's hand to move from the steering wheel to the gearstick. Observer's in the two different frames of reference would differ (by a very small amount, because of the low speed of the car) in their view of how long this takes. However, in the case that you refer to above, both the driver and the speedometer are in the same frame of reference - the frame of reference of the moving car - so time dilation wouldn't affect what is observed by the driver within the car. Further, what is being observed - noting the reading on the speedometer - isn't a time interval but a single event (unless you want to specify how long it takes to read the speed on the speedometer - then it could be regarded as an interval). In either case, what the speedometer reads would not be affected.

I do have one, of course. But I don't wear it often.

A relative speed of 60mph would give rise to time dilation, but the effect would be very small. Effects predicted by Special Relativity depend on the ratio v/c where v is the relative speed being considered and c is the speed of light. If v is very small compared to c, this ratio will be very small and so will the effect - time dilation in this case.

I was thinking about Everett's interpretation (what is referred to as MWI in the link that you have given). I am aware that Everett himself considered it to be falsifiable, but I haven't seen an example of testable predictions. quote: Many-worlds is often referred to as a theory, rather than just an interpretation, by those who propose that many-worlds can make testable predictions (such as David Deutsch) or is falsifiable (such as Everett) From here: https://en.wikipedia.org/wiki/Many-worlds_interpretation The link you gave was very relevant and interesting (although I have not read it all in detail). Thank you for including it. It seemed to focus on such things as the validity of axioms. The conclusion arrived at towards the end leaned towards scepticism rather than support for MWI (to put it mildly). On page 27: All of this suggests that Everett’s original program has degenerated, apparently beyond repair. Although the logical possibility of an MWI consistent with known physics cannot completely be excluded, it seems that the defining axioms of such a theory would have to be extremely ugly and arbitrary.

I've read a little about it since responding to the original post and have been surprised at how the effect has been observed. For example: The ebbing salty water flowing past London's Waterloo Bridge interacts with the Earth's magnetic field to produce a potential difference between the two river-banks. from: https://en.wikipedia.org/wiki/Magnetohydrodynamics I wouldn't have expected that to be measureable.