Dear Israel, this is the reply of part 1
''You: What I have tried... ...the problem
The argument of the snapshot has some issues. The first is that it is referred to macroscopic situations. In this sense I agree with you that you cannot tell the difference because macroscopic objects do not change too much from time to time. But at the microscopic level this no longer holds due to the continuous activity of the vacuum.''
This is not the point. The point is the lack of an equilocality relation between any two time slices. You cannot know if a quantum vacuum field is unchanging without a first reference frame to identify points (say, (x,y,z)=(0,0,0))
in different time slices. I have argued better for this in my response to your post in my essay (for anyone interested following the discussion,
Absolute or Relative Motion...or Something Else?. If you can provide a way of defining a preferred position by using the ZPF (this is the same as defining an equilocality relation) then you could finally see the PSR. But even if that is the case, one may argue that QM is background dependent and that GR´s main lesson is backgound independence such that the final theory of QG should be background independent. Again, any assumption will ultimately be used upon its usefullness, and this is something you have argued I fully agree.
'' One unrealistic situation that I found in the idea of a snapshot is that one cannot take instantaneous pictures of an event, basically for two reasons: First because the uncertainty principle will play the role in the outcome of the snapshot and second because an instant implies an interval of zero time which is physically inconceivable and experimentally unrealizable (although mathematically is possible). The idea that a snapshot captures an instant of time is misleading. One can only capture intervals of time different from zero (this is also stated in the uncertainty principle delta t delta E=h). And the problem comes from the mathematical representation of space and time as a continuum.''
You have made a good point, and I will explain why the snapshot argument is still valid in quantum domain. First, you argue that the deltaX*deltaP>h/2 part of the uncertainty principle make the task of even taking a snapshot impossible. But, if we are to consider quantum effects we should change the argument a bit: imagine we have a the information of the existence of a WAVE FUNCTION y(x,y,z,t0). A moment later the wave function has changed to y´(x,y,z,t1). Now we can only compare these wave functions if we have a procedure to indentify (x,y,z) points in different time slices. And the snapshot argument shows that the presence of a field defined over the whole space does not provide such an equilocality relation. One needs a background for that, and the ZPF, by being a field cannot be taken as a background (due to the snapshot argument). If by some procedure the ZPF can be used to define an equilocality relation, then everything is different. I invite you to think about it, if you can design such a procedure that would be very interesting.
Now adressing the deltaE*deltaT>h/2 part of your argument, I agree that we extrapolate our empirical experiences to conceving motion as evolving continuously on time. But if you feel too uncomfortable with that, we should change all QM, because QM describes the continuous motion of wave functions(or kets/bras, or field values, if you wish)!! The snapshot arguments goes well for exploring the fundamental properties of continuous motion.
''Weistrass assigned to each value of a variable t a corresponding value of the function x and defined a one-to-one correspondence between an element of a domain and its counterpart in the image group. By doing this he got rid of the problem of infinitesimals (small intervals). Which misled physicists by making them think that a physical object can occupy a point in space and time. Mathematically this is correct, but physically is inconsistent since physical objects occupy space intervals (volumes) and things occur within time intervals. In a point of time (interval of zero magnitude) nothing occurs, everything seems to be frozen and if nothing changes how can we justify motion?
If one assumes that space-time is physically continuous (composed of adimensional points) one arrives at the well know zeno's paradoxes. This is a topic I do not wish to address here. And like I said, despite these paradoxes, the continuum conception has been useful so far.''
Agreed. Nevertheless, it remains an interesting proposal to fill these gaps of the continuum assumption.
''You: but experimental evidence, at least to the extent that I know, has never produced such information... ...No experiment has ever revealed a preferred position, but a theory built upon a PSR would necessarily refer to such positions (I can't see how it could be done otherwise, if you have any idea please tell me). So this is why I concluded that the concept of PSR much be REALLY useful if we are going to introduce it.
There are many experiments claiming the detection of the PSR, but since the PSR is not even recognize by the mainstream of physics they are not widely known. My reference 17 (Eq. 3.14 for instance) shows that in principle the PSR can be detected. There I explain that the measurement of velocities is not a trivial task as most people think.''
That is very interesting. The detection of the PSR however must provide us a way to define a PREFERRED position. I haven´t read your paper in full detail I would be very grateful if you can provide a quick summary on the relation between your paper and preferred positions. Also, there´s a work of people in MIT who have captured the motion of light with a supercamera of 1 trilion frames per second (I must also admit I don´t know all the details of this experiment). I have posted the video in the response in my entry. It would be interesting if you can explain the relation of that with your work.
''Your arguments to refute the PSR are the same arguments that have been given against the PSR since the special relativity was put forward. I have laid down some arguments in my previous reply to you and I think that my essay gives some others. The special relativity has used the principle of relativity to establish that there are no PSR, to argue that there is no privileged observer for the description of physical phenomena. All systems of reference are equivalent. And I think this is misleading. They are equivalent not because there is PSR but because an experiment has the same result no matter its state of motion, absolute rest or motion.''
It´s a possibility. Now if we can do it without a PSR, why should we introduce a PSR? The discussion inevitably goes to the paradoxes the PSR assumptions solves according to you.
'' I am going to express how the principle of relativity should be really understood. Just keep in mind that above all physics is not only a theoretical science but also an experimental one. So, imagine an observer equipped with his measuring instruments at rest in the PSR, i.e., in vacuum/aether. He then performs a series of experiments to find the relations among the different physical quantities. From these results he arrives at the formulation of the laws of physics.''
Ok.
''He then put his whole equipment in a rocket and moves at a constant speed in relation to the PSR.''
How is he going to know wheter he´s at rest or moving in relation to the PSR? The PSR is invisible. (Again, if you can show how ZPF could provide a preferred position, then thing would become more interesting).
''Then, he performs the same experiments and the same operations in the rocket to find the laws of physics. For his surprise he finds the same laws as those he found while in the PSR. He then arrives at the reasonable conclusion that the laws of physics should be the same in any other system of reference and hence establishes the principle of relativity. So far so good, but here it comes the anxious question: What experimental reasons does the observer have to reject the PSR despite the fact that he cannot identify with his experiments whether he is really at rest or in motion relative to the PSR? One will easily realize that there is no experimental argument to refuse the PSR, since he knows that the same laws will be found everywhere.''
The question actually is the following: why even bother introducing the PSR if the information it provides is unobservable?? You can take any physical theory and introduce 15 dimensions for instance, and then say they are simply unobservable. Is this procedure reasonable? Yes if these new dimensions are useful for something, but if we can do it without the 15 dimensions we definitely should! The same applies for th PSR. Once again, our discussion should turn to the problems the PSR solve-we should not bother so much discussing wheter the PSR assumption is legimate by its own existence.
'' If our friend accepts the existence any other system, why should he reject the PSR? Do you have an experimental argument to refuse it?
No. Nor I have arguments to accept it. It is not wrong or right per se, all that really matters is its utility or lack of it. But again, if we can do it without the PSR (and without all kinds of unobservable statements) then we should.
Daniel
