Please can someone help me to get my head around the concept of momentum space?

OK, no one likes momentum space! I’m not sure that I’m keen on it myself – too technical. I felt I should look at it to see if it had any significant effect on a train of thought I was following, which went something like this:

The uncertainty principle says that we cannot know precisely the position and momentum of a particle at the same time; but can a particle actually be said to have a precise position, momentum or energy?

If a particle can, for example, be said to have a precise position, then, in principle, it would be possible to know the precise position of every particle in the Universe, and there would be no positional uncertainty. Would that not dispense with virtual particles?

Similarly, if a particle’s energy had a precise value, it would, in principle, be possible to know the precise energy content of the Universe, and there would be no zero-point vacuum energy.

Uncertainty must, therefore, be intrinsic to matter and energy; so when authors talk of measuring (e.g.) position, precisely, this must be an approximation. We could never make this exact measurement, because the particle lacks those exact attributes.

Personally I have almost no knowledge of momentum space. When I say almost I mean that I have heard of it, but not much more.

As to precision. You are correct. When somebody says they have made a precision measurement of anything then they are making an approximation. They may not really be aware of that fact, but scientifically you cannot make an absolutely precise measurement. And that really isn't a matter of the uncertainty principle. To make a measurement with absolute accuracy you have to have a measuring device with absolute accuracy. There is just no way to build such a device. It is obvious if you are making a measurement with something like a ruler, but even with something like a laser you still have some uncertainty. If you are measuring something with light waves then you have to observe interference between 2 waves. But you do that by eye-balling a line on a screen. Since the line will have a finite width you will have to estimate the actual position within the width of that line. So you still have an estimate, maybe a pretty good one, but still an estimate. In principle you can make finer and finer measurements, so you will have better and better estimates, but you will never be able to get absolute accuracy.

Of course once you add in the uncertainty principle you set an absolute limit as to the accuracy of any measurement. You cannot, in principle, get any better than (delta x) * (delta p) >~ h-bar. In this equation of course h-bar is h/(2*pi), that is Planck's Constant divided by 2pi. >~ represents greater than or approximately equal to.

Bill Gill

You neatly covered both types of uncertainty, there, Bill.

I should have been more precise. "Classical" uncertainty, which, as you describe, arises from our inability to produce measuring devices sensitive enough to make absolutely precise measurements is something related to our ignorance, rather than to the essential nature of the thing being measured. That can change as technology improves, so, in principle, we might eventually be able to make a precise measurement and thus overcome classical uncertainty.

Quantum uncertainty, on the other hand, seems to be part of the nature of reality. It is this that makes me wonder if, for example, a particle can be said to actually have a precise position or energy.

There would seem to be two possibilities for reality within the scope of quantum uncertainty:

(1) A particle has precise position, but we can never discover it.
(2) A particle does not have a precise position.

Of course, it may not be possible for us to actually discover the answer to this, but it would be interesting to know what current thinking in scientific circles is.

You leave out the other possibility a particle is nothing more than an illusion and you can no more measure it accurately than you can measure a rainbow, you have assumed particles are infact accepted as real solid things :-)

There are two common views of particles from scientists that fit the above description.

There is a group who would say particles are infact virtual and always have been wave packets. That is there is absolutely nothing solid or fixed about particles ever.

There is a group who would say particles are an illusion reflected into our physical universe they really are the proverbial rainbow.

I was taking one step at a time. It’s an age thing!

You will recall that above I suggested that a “particle may be no more than a contracted description of the full wave”.

Let’s look at the rainbow analogy: You rightly point out that it cannot be measured accurately, but if you photographed a rainbow with sufficiently good equipment, you could, in principle, locate every drop of water, every particle and every photon. Of course, they would no longer be there by that time, the illusion would have passed. Somehow you have to capture an instant in order to make your measurement.

I am wondering if the reality we perceive is just a series of “snapshots” of an overarching reality which we cannot grasp in its entirety, but can see only when it is reduced to these snapshots. I’m not suggesting a spiritual realm, just a cosmos that is greater than our Universe and may be quite different in essence.

I'm not sure that what we see is a snapshot. Or maybe it is a snapshot with a slow camera. It seems to me that what we see is more of an average. Kind of a smeared out view of what reality consists of. Then we put all these "snapshots" together and see a universe that is moving and evolving with time. This also makes it solid to our senses. I don't however think that this makes "a cosmos greater than our universe" necessary. It also doesn't change my feeling that the universe consists of what I can feel and see. Of course I also recognize that what I can feel and see is based on things happening at such a small scale that I can't see and feel them.

Now if I can just figure out what I am talking about maybe I will be able to say something with some meaning.

Bill Gill

I know that feeling!

That's more or less Julian Barbour's take on reality, which, to some extent, I like.

Regarding the idea that the cosmos might be greater than the Universe; I could really have expressed the same thought by saying that there is more to the universe than we can observe, and that we need something to enable us to make sense of it.

When it looked as though I might not get a response I posted the original question on a different forum. Here is a link, in case anyone might be interested in seeing how the other thread developed from the same starting point.

http://www.thenakedscientists.com/forum/index.php?topic=42432.25

Well, I agree that there is more to the universe than we can observe. But I don't think that what we can't observe is going to be much different from what we can observe. So by observing what we can observe we should be able to pretty much make sense of the whole thing.

Of course every time we think we are finally about to make sense of the whole thing a new observation comes along and throws us a curve. So I don't expect us to reach any final understanding in the immediate future.

Bill Gill

Does that mean you have serious doubts about a multiverse in which there are universes with, for example, different laws of physics from ours?

I don't have a good feel about a multiverse. I do have my doubts, but they are just based on a feeling, not on any real data. But at the same time that doesn't have much to do with our universe. If there is a multiverse then all the other universes are basically going to be disconnected from our universe, and I was talking about our universe.

Bill Gill

If Hajdukovic's idea turns out to be right the cosmos could be composed of a sort of "foam" of universes. Although each would be disconnected from all the others, is there any reason why one should not be visible from another, given the right circumstances?