# Why can't GRW theory be easily tested?

To me it seems that no matter if GRW theory is true, there would already be a lot of observations and evidence for/against it, since it will in quite simple situations make different predictions from e.g. orthodox Copenhagen interpretation including in variations of the double-split experiment.

As I understand it, GRW posits that super-positions exist and that all particles always have a small probability of collapse at any point in time (it has been suggested on the order of $10^{-8}$/sec but the exact value is not important for this question), whether they are measured in an experiment or not. Thus, when we have a quantum micro-system not being measured, the probability of a collapse happening is low due to the small number of particles, however, when the system is measured it becomes entangled with the measurement apparatus, which is a macroscopic object, and the probability of collapse within this apparatus is very high due to its high number of particles. Soon a spontaneous collapse will happen within the apparatus and this will in turn, due to entanglement, collapse the particles under investigation in the experiment also.

But I fail to see how this can likely be true or at least it should be easy to test if it was true: Consider the double-split experiment. From the point in time a particle passed through the slits (and is now in super-position) that particle will start having an impact on the surrounding particles, and the exact impact will depend on the route it will ultimately be seen as having taken. For instance, there will be gravitational affect on all surrounding particles (spreading at the speed of light, from my understanding), and there will also be effects due to the electric fields it creates in case of electrons etc. The effect will be a really small to be sure, especially for gravity and longer distances, but should in principle be there. So it seems the particle would become entangled with all particles and mass around it at the speed of light. This process starts immediately after the the particle itself has entered the super position (after exiting from the slit door) and before hitting the screen. If GRW is true, the super-position of the particle should quickly collapse because the particle will rapidly become entangled with so much mass that the probability of that collapsing is very high (corresponding to the measurement situation), i.e. the universe will heavily measure the particle.

So one could easily test this effect by having the photographic plate be some distance away from the slits and surrounding the experiment by a lot of mass close to it, like lead blocks or something like that, to increase the collapse-speed (note that the slit door in itself also contains a large number of atoms, and is very close to the point where the particle enters super-position, so a lot of entanglement should happen here as well in the standard experiment). If GRW is true, things could be set up so the particle should not be able to reach the photographic plate before it collapses due to the overwhelming entanglement on its way, exceeding the amount of entanglement that would occur from hitting the plate itself and which is usually enough to cause collapse in the standard experiment - thus no interference pattern would be seen. By varying the amount of surrounding mass and/or track length it might even be possible to determine the per-particle, per-second collapse rate. Has any experiments been done along those lines?

One argument I could see against this line of reasoning would be something like "Oh, but the other interpretations will predict the same thing, they will just consider all the lead blocks etc. as a sort of measurement device" or maybe invoke decoherence to explain how the super-position would look like it collapsed in all interpretations. But I fail how to see this objection can be true because in no ordinary treatment of the double-slit experiment are the materials that form part of the experiment (slit door, electron gun, wires, whatever) considered a measurement apparatus or accounted for (be it with respect to decoherence effects, GRW-like or other effects) and clearly the effect is not big enough to cause the collapse to happen before hitting the screen, since otherwise the experiment would never have shown an interference pattern to begin with!

So it seems other interpretations only count the artifacts that plays a role in delivering the result to the experimenter as part of the measurement apparatus that can cause collapse (i.e. the objects that form part of the von Neumann chain). However, GRW should from its formulation consider ALL material in the vicinity as candidates for triggering spontaneous collapse and this should cause experimentally observable differences as described earlier?

I'm something of a novice when it comes to GRW, but my understanding is that an individual particle's gravitational interaction with it's surroundings is too small to create a significant chance that the wavefunction will collapse. With a macroscopic object consisting of around 10^20 particles the collapse would be nearly instantaneous and the theory would be more or less proven. However with current technology that form of testing would realistically have to wait quite some time before the proper technologies became available to prove or disprove the theory. Some thought experiments have been devised involving mirrors in superpositions, but again the mirrors would need to be of a respectable size. I haven't had enough experience in the matter to comprehend the last two paragraphs of your question, but I hope what little I have to offer was of some help to you.

According to Schlosshauer's review (Annals of Physics, 321 (2006) 112-149), "no positive experimental evidence exists for physical state-vector collapse", so why should we expect experimental confirmation of GRW spontaneous collapse?

Another thing. Suppose you conduct such an experiment and find no collapse with frequency of $$10^{-8}$$/s or higher. Then a fan of GRW can tell you that his favorite theory is still correct, but the frequency of spontaneous collapse is, say, $$10^{-10}$$/s, and so on. This can be a long story...

• There is an experimentally-established upper bound on the time and distance scale of GRW; this upper bound will be reduced as experiments become more sensitive. There is also a lower limit, below which the GRW process would be too infrequent to serve as a solution to the quantum measurement problem. If the upper bound ever reaches the lower limit, then the process is ruled out. In short, this is physics: a search for evidence, not mere unmotivated opinion. – Andrew Steane Nov 18 '18 at 9:43
• @AndrewSteane : So could you please give a reference for the lower limit? – akhmeteli Nov 18 '18 at 9:49
• Brian Collett and Philip Pearle, Foundations of Physics, Vol. 33, No. 10, October 2003. (More recent refs will give tighter upper bounds but when I looked just now this was the first I found with a statement about a lower limit too.) – Andrew Steane Nov 18 '18 at 16:09
• @AndrewSteane : Thank you very much for the reference. They do offer an estimate for the lower limit, but it does not seem reasonable (moreover, they say themselves that their "theoretical constraint" is fairly rough): their criterion seems to be "to account for the world as we see it." They define a situation where they believe what we see contradicts quantum theory. However, our vision typically works in air, and, according to their own article, spontaneous collapse diffusion distances are much reduced due to collisions with air molecules. And there are other problems with their approach. – akhmeteli Nov 18 '18 at 18:48
• By 'as we see it' they wish to include all the various experiments, including those in vacuum. But more generally, any model which involves a spontaneous collapse process will be deemed irrelevant to the quantum measurement problem if its effects are too small to influence something at the time, mass and distance scale of, for example, a household cat. It follows that such models are amenable to being ruled out, in principle, if experiments can reach a specific finite degree of sensitivity. – Andrew Steane Nov 20 '18 at 10:05
1. ANY interpretation of QM must allow for all the gravitational and other interactions with surrounding material that you mention. Let $$|L(t)\rangle$$, $$|R(t)\rangle$$, be state vectors for motion via left and right slits in a Young's slit expt. As a result of the interactions you mention, in practice one has

$${1\over\sqrt{2}} (|L(0)\rangle + |R(0)\rangle) |env_0\rangle \rightarrow {1\over\sqrt{2}} (|L(t)\rangle |env_1\rangle + |R(0)\rangle |env_2\rangle)$$

where $$| env_i\rangle$$ refer to states of the surroundings and I mean here the state BEFORE the particle reaches some final detector such as a camera or screen. If $$\langle env_1|env_2\rangle \simeq 1$$ then this will not affect the interference, and any GRW-type collapse of the environment will have no impact on the interference. If $$\langle env_1|env_2\rangle \simeq 0$$ then the interference will vanish whether or not there is GRW-type collapse.

1. Regarding detectability of GRW process, it is a definite prediction that can be experimentally detected, like other items of physics such as electric dipole moment of the electron. It is simply that experiments have not yet reached the precision required to learn whether or not such an effect is large enough to impact on the quantum measurement problem.