Um, no. One sees both the distance and time as larger. The other sees both the distance and time to be smaller. That's the onlly way the ratio can be the same for both.
It's what comes after 6 hours of writing until 5AM for work. But the point is that time dilation and length contraction are
1) Both based on an invariant
2) Both deal with physical properties that can be measured by the same observers.
In other words, Alice (or whoever is in the train) "sees" light travel straight up and down, and Bob sees it traversing a triangular path, they both measure the same speed of light, which means that they must disagree over the distance and time in a particular way, and moreover a way that allows us to reformulate the relativity of mechanics into that automatically satisfied by (properly writing down) the equations of EM.
This is why Rovelli is so irritating here. And it's not just me. As he's become more involved in quantum foundations, the kind of slipshod approach that is basically required in quantum gravity becomes a serious hinderance. If you try to correct your critics in the literature by saying that you mean X not Y, and then fail to keep to your own terms, usages, or claims a few paragraphs down, then the conflation of one fundamentally different type of observer disagreement with whether or not there can be observer independent properties when the theory predicts "no" (recall that these extensions and tests to Wigner's friend are akin to what Bell did to Bohm's reformulation of EPR- make it into something that can be empirically tested because we can't even assert that single experiments in QM are actually meaningful without running into objections raised by those like Ballentine on the one hand or the intellectual descendants of Bohr (or of Wheeler) on the other (and there are several more "other hands" here).
The relativity goes both ways. Each sees the other's measurements as dilated for things moving in the other system.
I'm assuming "sees" here means "considers"?
Which actual measurements do they disagree about? Do Wigner and Wigner's friend actually disagree about the spin when they get together to discuss the results? No. They only disagree about the time of the collapse.
Wrong. First, in the realization linked to (Liefer calls this "Wigner's enemy") the friend was a bit of information that could be reversed or erased using e.g., weak measurements or partial measurements and something like spontaneous parametric down-conversion.
This is the scenario:
First, recall Bell's reformulation of Bohm's version of EPR: you have some (not necessarily quantum) two-level or bipartite system that becomes space-like and time-like separated. It could be two correlated particles with spin that decayed from a spin-0 particle, or two envelopes with notes saying "Yes" for one and "No" for the other. It doesn't matter. The idea is to have a common source for the "information" sent to two "labs" such that, when the "information" gets there Alice can open her envelope or measure polarization or whatever. So can Bob.
Now, Bell then assumes that there are parameters λi (e.g., λ1 and λ2) such that, whether or not we can determine what the parameters represents or if they can be measured or just about anything, we can determine that it is at least possible to explain the correlations that between Alice and Bob's measurements by a local source (the original system that generated the "information" sent in the form of envelopes or what have you).
Then pick a useful relation between the measurement outcomes for your purposes (or one determined empirically). See if it can be explained in terms of these hidden parameters. For the case even of many quantum systems, there is a way to reproduce the correlations classically. You can show that, in order to have no classical explanation, you must violate an inequality generated e.g., by a set of assumptions that include object definiteness, which is to say that while we may not know which envelope contains the card with "Yes" vs. "No" or |0> vs. |1>, the system had this property and the correlations are due to the original, local interaction.
Then Bell shows that using tripartite quantum spin systems one can violate such an inequality. In other words, no such λ's can exist.
In the Bell-type Wigner's friend, or at least this one (Brukner's is a bit different, and Renner's is so different it doesn't involve Bell-type statistics at all), the friends Charlie and Debbie are the two systems that would correspond to the decayed atoms or envelops. The measurement settings Alice and Bob pick (x and y) are the local hidden variables. The outcomes A and B are the same as in the Bell set-up, corresponding to Alice's and Bob's measurements, respectively.
Now, you make the assumptions that the conditional probability of reversing/erasing the "friends" measurement is the same at least approximately the same as them not making measurements: the probability P_under reversal "undoing" the friends measurement_ (A, B|x,y) is roughly equal to the probability P_no Charlie or Debbie_(A,B|x,y)
That is, you assume that you can choose to use Charlie or Debbie's measurement or not, but if you choose not to allow them to measure (experimentally realized by not having the measured photon interact with "Debbie" or "Bob" via that path), then you should be able to treat this as if they didn't interact with the system. That is, if you don't measure the photon produced via no spontaneous parametric downconversion that takes the D or C route, or rather you erase the path/information such that it is as if you are simply making a standard measurement, then it shouldn't matter that D or C existed as a route at all. You should be able to assign truth values (akin to the object definitiveness from Bell experiments) to your own measurements. If your measurement uses information about the Charlie and/or Debbie path, then then you should still have (and will have) a definite output for that case (x & y both are 1) while for other values the choice is made to erase the photon from the SPD that interacted with the C & D path, measure the ones that didn't, and obtain a definite outcome consistent with this operational procedure.
You can't. It doesn't work.
The disagreement is about the time of collapse. But which result of an actual measurement do they disagree about when they get together? There are measurements that one or the other saw as being in a superposition, and so undetermined, but no actual disagreement with actual results is ever the case.
You can't get disagreements about the actual results (which is why Rovelli is continuing to dig himself into this whole that I wish he would stop), which is why Rovelli's relativity analogy breaks down completely. You can't perform the measurements of the same system. In the classical Wigner scenerio, you get one result if you ask the friend, and another if you put the friend into a superposition state.
For many physicists, basically all measurements in QM that attempt to determine something like the state of the system in the sense discussed here are contradictions to QM. That's because in QM, evolution is unitary. The projection postulate, Born's rule, collapse, reduction, or even "update" are all non-unitary and are
ad hoc. They contradict the predictions for the dynamics of all systems in QM. .We don't say, that of course (unless we subscribe to a no-collapse interpretation). We say that measurement involves a different process, and sweep under the rug the fact that the probabilities that we use when we claim that a measurement outcome is predicted by QM come from an ensemble of measurement degrees of freedom that can't (unlike classical ensembles) be decomposed even in principle into the statistics of single states/measurements.
In short, we have to use a series of ingenious methods and measurement schemes for each different system in order to be able to talk about the probabilities associated with it, but these are determined not by QM (which, again, describes systems via unitary evolution or in the more general operational approach in terms of CPTP maps, where we likewise replace the states with density operators and the projection-valued measurements with POVMs). So we have "predictions" QM makes that we determine by using QM right up until we extract information. Because we don't have a theory that accounts for measurements, we can't use QM without being able to talk about measurements, we get a contradiction if we treat the measuring device quantum-mechanically (that's what Wigner's friend is about, except that it is intended to be more drastic), so we simply tack on another type of state evolution to quantum theory.
Put more simply, we can pretend there is no contradiction, and then simply see what the measurement outcome would be if we treated the mesurement apparatus quantum mechanically the way we would if we treated it like one in the lab: in terms of the Hilbert ray we'd obtain from the product of the Hilbert spaces and rays corresponding to System (tensor product) Apparatus.
That's Schrödinger's cat and Wigner's friend. QM predicts something never seen. Hence, it contradicts itself.
Or we don't say that and we think about measurement as part of QM that we haven't worked out yet. One way to go about this is to try to think about how the measurement process works, generalize it to an operational framework that can be used without deciding on an interpretation, and then apply it in the development of no-go theorems and the like as well as their experimental realizations.
But what is the actual contradiction? What measurement, that they both agree is not a superposition, do they disagree about?
Depends. Firstly, if one is talking about the Frauchiger-Renner experiment, then it is about self-measurement (an extension of the Deutsch version). If it is the standard EWFS of Brukner, then the actual measurements will disagree as this version is about obtaining information from the friend that we can later compare (in principle). In the classic Wigner's friend, the only way we wouldn't get a contradiction is if two friends walked out of two labs with both outcomes (or, more friends, labs, and outcomes). In the Griffith version, the contradiction is in the ability to assert if an event is observed, it happened.
