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Offline yor_on

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An essay in futility, too long to read :)
« Reply #400 on: 22/10/2011 05:43:42 »
And all of this makes HUP so incredibly important to me. It's a principle for 'motion' without 'motion', it allows things to be 'manycolored' even though we know that, when 'falling out', there can only be one color existing 'historically'.

It does not involve a arrow, it does not discuss motion, although I used it as a weird analogue :) It's just a state of indeterminacy. And it's close to the 'probability functions' we discussed before. They both point out one thing, that we won't know until we measured.

(Now you can point out that we won't know all qualities of our measurement, simultaneously, even after measuring according to HUP, and that is true. But it's weirder than that, by choosing one of those properties, you actually can be seen as 'forcing' it to come true, making its probability a 'certainty', and that is what I'm aiming at here.)

You can argue that the probability for the moon to be there are as near certainty to make it meaningless to question. But the beauty of it is that there still will be a probability of it not existing, however small. We live in a universe of probability. But macroscopically we don't find it indeterministic, and that should have to do with 'scales'. Does a greater scale imply a larger quantity?
=

What about a Lorenz contraction?
And the way we expect it possible to create energy (radiation) from relative motion.

Scales are weird.
« Last Edit: 22/10/2011 06:22:16 by yor_on »
 

Offline yor_on

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An essay in futility, too long to read :)
« Reply #401 on: 22/10/2011 06:00:03 »
Vacuum fluctuations is not anything fluctuating. It's that exact state of indeterminacy in where it has a probability of 'energy'. And a vacuum is classically 'empty', without 'energy' as I see it. Both statements works together. You will only find a vacuum 'effect' as the Casimir effect when introducing a relation that disturbs that 'emptiness' at a quantum scale.
==

And the idea of a negative 'energy' can't be true in a universe steered by conservations laws. If it was we should lose 'energy', and as far as I know we don't. What we have instead is symmetries, anti-particles/particles for example. Exchange the idea of 'negative' for indeterminacy, and I will agree though. Not that they are the same, but its as close to it as I can come for now. Except in the case of there being proved that 'negative energy' really exist. And the proof for that would be something annihilating something else leaving no trace, and no radiation/energy.

==

Defining 'gravity' as 'negative energy' makes no sense to me. Imagine a gravity well, imagine one photon falling into it, another 'climbing' it. Where is the negative result? They will take each other out, and what 'energy' one 'gained' relative the observer, the other one lost. If it was truly 'negative', all universe would be one single gravity well pointing 'up', no matter your direction, everything getting red shifted, but I don't see that?

('Negative' is in this case the idea of something 'losing energy' relative 'gravity'.)
« Last Edit: 22/10/2011 06:47:10 by yor_on »
 

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An essay in futility, too long to read :)
« Reply #402 on: 22/10/2011 23:53:01 »
So, what is time? Keep coming back to that one don't I :)

I don't really know, to me it is something giving us a temporal direction, but I believe it uses a 'clock', and that is radiation. Assume you're 100 lightyears away, at rest relative me on earth. You use your laser and send me a light pulse. How long will it take? Now you stand up and start to walk away from my position relative your planet, as you do you send me a new light pulse. What do you expect the time difference to be, walking at 10 meters a second away from me, if compared to the time it would take that light pulse you sent sitting down, at rest relative me?

I've seen some reasoning around the idea of the sheer geometry making a 'time dilation' larger,  in the definition of your 'now', relative mine 'now', displacing it into the past, and if you went towards me displacing your now into my future. That's a really weird way of defining 'time' to me.

That light pulse you sent, will be slightly displaced by the durations differing as you sent it, as defined from your frame of reference. But the speed of it will be the same, and the time dilation those ten meters made negligible, as I think of it. Why would the distance between two frames, at rest with each other, change the time dilation? It's a geometric idea that light will kill, when sent.

Simply put, lights speed is 'c', the distance measured between two frames of reference, at rest relative each other, must give the same measure from both frames. A motion at 10 meters/s will produce a slight time dilation, but it shouldn't matter if those frames of reference is one mile from each other, or a hundred light years, as I see it.

Relative motion is just relative motion. It doesn't care about the distance measured between those frames of reference. It's lights invariant speed that defines a time dilation, relative motion and mass (energy).
=

But if you have a proof of it being different, feel free to correct this. And not 'geometry' per se, a proof.
« Last Edit: 23/10/2011 00:13:57 by yor_on »
 

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« Reply #403 on: 23/10/2011 00:10:12 »
So tell me, do you assume all stars and planets in this universe to be 'at rest' relative each other, in that uniform motion they should have? No matter what 'energy' they may have? Relative Earths uniform motion? If so, do you assume that they all have a same 'speed/velocity'?

The question here is, assume that stars have different 'speeds/velocities' relative each other, but also that they are 'at rest' relative each other, having a uniform motion. If a 'energy' is found relative that 'speed' as defined relative Earths 'speed/velocity', will they then have a time dilation relative Earth?

And, can they then be said to be 'at rest' relative Earth?
=

And as mass is a equivalence to 'energy' that is enough for proofing different 'energies' here.
« Last Edit: 23/10/2011 00:25:03 by yor_on »
 

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« Reply #404 on: 23/10/2011 00:19:37 »
To me it doesn't matter what speed you define them, but if you think that 'energy' is related to relative motion, and also localized to whatever object you define to move relative you.

It must..

Then there is a new definition of 'being at rest' too. In that definition you will now have to define a 'absolute speed scale' for the universe to know that 'energy' localized to whatever object you measure.
 

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« Reply #405 on: 23/10/2011 06:40:52 »
Maybe I'm angling those questions a little. But it comes back to what that 'uniform motion' should be seen as. I assume here that being 'at rest' should mean that we have no time dilation and that the distance should be the same for all observers. But if we consider that all mass should be different, you will have a time dilation and Lorentz contraction in that fact only. If you then also consider the possibility of the relative motion to differ you will find that you will get different answers for it, depending on your choice of coordinates, earth as being 'still' for example.

So a uniform motion can not be assumed to present a same time dilation, Lorentz contraction, and I don't need to consider 'potential energy/relative motion' at all, only mass will do.

So I'm wrong in assuming that 'at rest' should represent a 'system' where both parties find distance, and time dilation, to fit. It must differ with mass. But it is still so that all uniform motion is impossible to differ in a black box scenario.

This one is more tricky than I first though.

The question becomes two folded. From the point of 'locality', which is the one I prefer, this is uninteresting. Because it doesn't matter what you find the time dilation to be, or distance. It's my definitions that are true for me, and the only thing we really share is a state in which we both will get the same results from experiments done in a black box scenario. But if I consider it from the idea of a 'whole SpaceTime' where simultaneity defines the reasons why we measure it differently?

I need to think about this one.
 

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« Reply #406 on: 23/10/2011 07:10:27 »
Maybe I can put it like this? To me there are some properties of the universe that are 'common'. 'c' is one, being 'at rest' is another, gravity/accelerations is a third. Those binds this universe together, and to me they seem to be the closest thing to what might be seen as a collective frame of reference. And it is the way they present us with a universe that makes us think we 'share the same universe'.
 

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« Reply #407 on: 23/10/2011 19:20:17 »
Let us have a look at another thing.
'Energy'.

Energy isn't 'here', and it isn't 'there' either. The purest expression of it, as I know, that we can observe is 'radiation'. And the reason why it is 'pure' is our mainstream definitions of a 'photon' as being intrinsically massless and timeless.

But it is also so that 'energy' is 'mass'.

"The mass of a proton is about 938 MeV. It consists of three quarks, each of which have a mass on the order of 3 MeV (more or less, not very accurate.) There is a huge discrepancy between 938 and 9. The remainder of the mass of the proton is the potential and kinetic energy of the gluons holding the whole thing together. The correct vision of a proton is a little subatomic gluonic lightning storm, buffeting three nearly insignificant quarks. "

?
 

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« Reply #408 on: 23/10/2011 19:25:25 »
Potential 'energy' huh?

The same we should see in that relative motion? If I can't seem to define it for uniform motion, what makes you expect it to be there? Can you define it? Maybe it's not 'energy' at all, maybe it's some sort of 'nested' geometry?

But why would that give 'forces'?
Accelerations and decelerations, what are they?
 

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« Reply #409 on: 23/10/2011 19:36:05 »
How about this then?

Assume that we have 'network' of borders, at a very small scale. They define something that is 'still'. Then as we scale it up the borders disappear and transforms, introducing us to the 'arrow of time' we know. The 'arrow of time' allows us a 'illusion' of motion, as well as 'energy'? And what we see is a effect of 'scales'. Too weird? Maybe.

Don't take 'illusion' too seriously here. It's no illusion from where we are, we built all of physics from the 'reality' we see and can experiment about.
 

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« Reply #410 on: 23/10/2011 19:41:49 »
But then we have HUP, and indeterminacy.

A 'still motion' not in time.
=

If there is 'borders' at a microscopic plane, then what is HUP doing there?
 

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« Reply #411 on: 23/10/2011 20:11:53 »
If space is observer dependent, will the 'flatness' we ascribe to the universe be 'flat' in all observations? And what makes you sure that one observation is more 'true' than another? If uniform motion, as I see it, is a 'universal description' of something shared by all observers, no matter their relative motion. Then we can imagine someone at a very high velocity, still being in a uniform motion.

What would he see? A 'flat' universe?
« Last Edit: 23/10/2011 20:17:24 by yor_on »
 

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« Reply #412 on: 23/10/2011 20:19:14 »
When we imagine a 'density' of 'energy' we actually assume that there must be a border. Without a border a constant density is meaningless. But all of our definitions has to do with the way we experience things. We find borders everywhere on Earth, that can of tuna represent a border, differing the containments of it from the space outside that can. So we use that terminology when trying to understand the universe.

But it doesn't make sense. Look at our proposals. We come from a 'dimension less' point, we assume a 'even density' to it, then we assume a inflation to 'split' this density into the clusters we see today, being the same in every direction. We define it such as the 'distances' we measure is 'real', and that 'space' exist.

If you have a 'dimension less point', what makes you define what we have now as something different?

If there is no 'arrow of time', what makes you expect that you can deduct it.
« Last Edit: 23/10/2011 20:30:08 by yor_on »
 

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« Reply #413 on: 23/10/2011 20:59:49 »
I find this one to present a fairly understandable description of what we see, and think us to know about the universe today. The Expanding Universe

But it does not discuss the observer dependence.
 

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« Reply #414 on: 24/10/2011 04:16:33 »
For those of you wanting to argue that this observer dependence only is applicable to relativistic speeds, and neutron stars/Black Holes, check on those atomic clocks that NIST used.

I expect them to exist on a Planck scale, and if so, not to be ignored in any description of a universe or quantum realm. The question is naturally also if you see Einsteins length contractions and time dilations as being true descriptions, but if you read this far I suspect you do :)

The idea of 'gravity' as a negative 'energy' do make for a balanced universe, but it also implies that we would have two opposite principles. But space do not negate 'energy', so to define it as 'negative' seems wrong to me. Once again I find myself liking the idea of 'symmetry' better.

So what was that 'dimension less point', maybe at Planck size, as that is where we start make sense of the physics we have. A symmetry break? Does a symmetry break crave a 'distance', or is that our definition of it from the inside?
 

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« Reply #415 on: 24/10/2011 04:28:56 »
Assume that it is a symmetry break. Then what it shows us are durations ordered into a causality chain. What we define as a 'arrow', as in 'clocks', could then be the way we get our descriptions from, as it is from that we define a 'distance', as well as anything else you find making a 'change'. It's like having two simultaneous 'realities', one where the arrow defines our descriptions, another where 'time' has no meaning and where this 'symmetry break' just is.

That would fit the way different manipulations can contract the 'SpaceTime' we observe. But it's just a thought, nothing I can prove.
« Last Edit: 24/10/2011 04:58:52 by yor_on »
 

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« Reply #416 on: 24/10/2011 04:37:47 »
But if it was so, then why would that 'arrow' always be the same to you? If we set for example 'c' as some limit, like a border for our SpaceTime. Why would that (invariant) clock still exist near the limit?

What I mean is that the 'arrow' still will be there for you, your 'intrinsic measure of time' no different from before, if we define it as your watch relative your heartbeats. That it, to me, is equivalent to our description of radiation as a constant, makes no difference for this. What makes 'time' and its 'arrow' so invariantly, locally, consistent?
« Last Edit: 24/10/2011 05:03:07 by yor_on »
 

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« Reply #417 on: 24/10/2011 04:52:00 »
If it so that your intrinsic measure of life is constant, no matter where you are and do, then there is a arrow of time. Meaning that it contain a limited amount of durations (life span) that never will differ from your frame of reference. I assume this to be the truth. But that 'constant' makes all you see around you adapt relative motion/mass/gravity/energy.

So whatever 'time' is, to my eyes it's a local phenomena first, and a 'shared 'universal'', only in that restricted sense of us all experiencing it in the same (local) manner.
« Last Edit: 24/10/2011 04:56:13 by yor_on »
 

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« Reply #418 on: 24/10/2011 05:14:54 »
And one weird thing more. Lately I've started to wonder about if 'scales' and 'distance' is the same? How do you define a 'scale'? :)

Dam*d if I know, I mean we have them, and we use them. That is what makes that 'quantum spookiness' visible to us. If you, as I, assume that 'dimensions' isn't something you 'glue together', but really exist as whole descriptions? That is what Einstein assumed too in his definitions, as I think of it, at least when presenting the idea of a SpaceTime.

How can I differ a contraction/magnifying, as in expanding a volume of interest, from a contraction/magnifying perceived in a relative motion/mass/gravity/energy?

I'm sure there must be a way, but I can't see it. Even if they are the same we percieve it differently. And now I'm sounding :) quite 'wacky'.

It's about geometry, and 'space'.
==

And before you tell me that there is no 'magnifying' in relative motion :) That depends on your relative motion, and mass, as compared to another frame of reference, as I think of it.

It's all about light, isn't it? And the way it conveys 'information'.
« Last Edit: 24/10/2011 05:35:34 by yor_on »
 

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« Reply #419 on: 28/10/2011 04:21:21 »
So, if 'c' is the clock, what does it make time?

This is my view.

I see time as having both a value and a direction. And that is not wrong, although not the usual way to define it. Normally time is defined as a scalar, having only a value. From a entropic point of view in where you expect 'time' to evolve in each point, according to some entropic principle, you might want to argue that this is the best definition.

But my view is that time has a lot to do with 'c', and using that we will find that although we all find others 'time' to vary, we also can agree on that the 'local clock' we then use is, in some means, 'universal', meaning that all 'local frames' have a same defined 'ground state' as defined by 'c' locally (clock).

And that gives SpaceTime a 'direction', not only locally.

You might ignore the universality there, I usually do, as I define it all locally to keep it simple. But on the other hand, if that 'ground state' didn't exist we would have a lot of trouble assuming that 'entropic view' for example, as we then might find that there was no clear definitions of 'entropy' as in a radioactive decay relative another expected to be the 'exact same'. Also we have the fact that all atoms behave the same, and that one interaction with one atom is interchangeable with a same action on another 'same' atom, etc.

So it is a important principle to me, and if we let our imagination run free for a moment all points in SpaceTime then should be 'moving locally' at a same temporal speed/rate, but in this case also describing a (universal) vector at that 'ground state'.
 

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« Reply #420 on: 30/10/2011 16:39:44 »
Heisenberg Uncertainty relation.



"Note that the indeterminacy of the microscopic world has little effect on macroscopic objects. This is due to the fact that wave function for large objects is extremely small compared to the size of the macroscopic world. Your personal wave function is much smaller than any currently measurable sizes. And the indeterminacy of the quantum world is not complete because it is possible to assign probabilities to the wave function.

But, as Schrodinger's Cat paradox show us, the probability rules of the microscopic world can leak into the macroscopic world. The paradox of Schrodinger's cat has provoked a great deal of debate among theoretical physicists and philosophers. Although some thinkers have argued that the cat actually does exist in two superposed states, most contend that superposition only occurs when a quantum system is isolated from the rest of its environment. Various explanations have been advanced to account for this paradox--including the idea that the cat, or simply the animal's physical environment (such as the photons in the box), can act as an observer.

The question is, at what point, or scale, do the probabilistic rules of the quantum realm give way to the deterministic laws that govern the macroscopic world? This question has been brought into vivid relief by the recent work where an NIST group confined a charged beryllium atom in a tiny electromagnetic cage and then cooled it with a laser to its lowest energy state. In this state the position of the atom and its "spin" (a quantum property that is only metaphorically analogous to spin in the ordinary sense) could be ascertained to within a very high degree of accuracy, limited by Heisenberg's uncertainty principle.

The workers then stimulated the atom with a laser just enough to change its wave function; according to the new wave function of the atom, it now had a 50 percent probability of being in a "spin-up" state in its initial position and an equal probability of being in a "spin-down" state in a position as much as 80 nanometers away, a vast distance indeed for the atomic realm. In effect, the atom was in two different places, as well as two different spin states, at the same time--an atomic analog of a cat both living and dead. The clinching evidence that the NIST researchers had achieved their goal came from their observation of an interference pattern; that phenomenon is a telltale sign that a single beryllium atom produced two distinct wave functions that interfered with each other.

The modern view of quantum mechanics states that Schrodinger's cat, or any macroscopic object, does not exist as superpositions of existence due to decoherence. A pristine wave function is coherent, i.e. undisturbed by observation. But Schrodinger's cat is not a pristine wave function, its is constantly interacting with other objects, such as air molecules in the box, or the box itself. Thus a macroscopic object becomes decoherent by many atomic interactions with its surrounding environment.

Decoherence explains why we do not routinely see quantum superpositions in the world around us. It is not because quantum mechanics intrinsically stops working for objects larger than some magic size. Instead, macroscopic objects such as cats and cards are almost impossible to keep isolated to the extent needed to prevent decoherence. Microscopic objects, in contrast, are more easily isolated from their surroundings so that they retain their quantum secrets and quantum behavior." From Uncertainty Principle:

Decoherence?

Where, and how, do I define that?
Through scales?

Number of atoms?

Einstein Bose condensates?

If I take a system of atoms (gas) and chill them, what do I get? Is there a limit to that, or is it just a practical question about what we can do?

I don't like the idea of 'virtual particles' that much any more. But I'm starting to wonder a lot about HUP.
« Last Edit: 30/10/2011 16:41:37 by yor_on »
 

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« Reply #421 on: 30/10/2011 17:37:09 »
In what way do decoherence define the 'bridge' between what we see macroscopically versus microscopically? Does it say anything about temperatures? Do they matter at all? (yeah I know, a pun)

The Role of Decoherence in Quantum Mechanics.

One more thing, did Einstein demand a time symmetry (the symmetry of physical laws under a time reversal)? That is, did he think that time was a symmetry that could be turned both ways? What I'm wondering about is whether he saw this as a primary mathematical solution, or one that already exist in our universe? There is a big difference between what we can prove by experiments, relative by theory as I see it. And symmetries is one of the strangest, at the same time as they seem to me as one of the most obvious, things that I know of.

 

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« Reply #422 on: 31/10/2011 06:58:40 »
So if you make some 'system' to study, we then need to define borders for it to state that nothing interfere with its wave function. And one way is to use temperatures, as a condensate, right?

What more does this lead to? Many worlds theories is one, in which every interaction is taken, although only one 'visible' to you observing, or Feynman's in where 'interference' kills of those other possible outcomes, leaving only one realizable. The later one avoids those other possibilities and so is easier to handle, from the idea of conservation laws. I expect the first to lean on the assumption that in a 'superposition' conservation laws can't exist, only in the realized outcomes.
 

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« Reply #423 on: 01/11/2011 05:47:55 »
So let's look at time symmetries again. Using my way of looking at it radiation is a 'clock' giving you a same duration locally. That gives us a 'same' surface of durations. 'Time' as such is something more than that though, we expect it to construct causality chains, don't we? The idea is that it do have a direction and that we by backtracking that direction can draw conclusions, and build models, of what's going to happen in the future.

From entropy's side it builds on that everything seems to have a direction from 'ordered' to 'unordered'. That things move from what we define as useful energy, to 'unuseful' seems true enough. If you like, we could say that we have two states of high entropy (evenness/order). One at the beginning, according to the Big Bang, and one at the 'end' according to 'entropy'. That's also a definition in where we expect a 'heat bath' for the cosmos as I understands it, making 'heat', not 'energy' per se, becoming a ultimate definition for a 'final stage'.

So is it true? That we can turn all 'interactions' around, and that they then will give us a 'same origin' as we remember it to have been when we 'started'? Nope. It doesn't seem to be true. CPT symmetries shows us that some interactions, k-and b-mesons for example, will have a CPT- invariance but not under T (time) alone. It also can be shown with mesons that you by their behavior can know if they are going 'forward' in time, or 'backward'. The idea of all 'stuff'  being able to be played 'backward and 'forward' in 'time' is particularly expressibly described in so called Feynman diagrams.

Some physicists, most studying quantum levels, as I get it, ignore this as a unfortunate exception to a rule. Then again, what is a 'history', and 'virtual particles'?

« Last Edit: 01/11/2011 05:56:57 by yor_on »
 

Offline yor_on

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An essay in futility, too long to read :)
« Reply #424 on: 01/11/2011 08:21:59 »
From entropy's side all processes should be irreversible, in that they all cost some 'energy', described as heat loss mostly, as I've seen. So you can't really turn back the process to its original state. As I too often state, I don't know what 'energy' is, except something describing transformations. But somehow the idea of a universe in where nothing gets lost must contain whatever disappears in a transformation. Which then points to 'heat' thermodynamically.

'Virtual particles' is a very faceted idea that hurts my head. Over the years it seem to have gone from an idea to a 'fact', without no experimental evidence I know of. The idea of the Casimir effect proving it is, as far as I know, still disputed. I've seen it explained as a effect of the matter involved, as well as of 'virtual particles'.

"Virtual particles must not be considered real since they arise only in
a particular approach to high energy physics - perturbation theory
before renormalization - that does not even survive the modifications
needed to remove the infinities. Moreover, the virtual particle content
of a real state depends so much on the details of the computational
scheme (canonical or light front quantization, standard or
renormalization group enhances perturbation theory, etc.) that
calling virtual particles real would produce a very weird picture of
reality.

Whenever we observe a system we make a number of idealizations
that serve to identify the objects in reality with the
mathematical concepts we are using to describe them. Then we calculate
something, and at the end we retranslate it into reality. If our initial
initialization was good enough and our theory is good enough, the final
result will match reality well. Because of this idealization,
'real' real particles (moving in the universe) are slightly different
from 'mathematical' real particles (figuring in equations).


Modern quantum electrodynamics and other field theories are based on
the theory developed for modeling scattering events.
Scattering events take a very short time compared to the
lifetime of the objects involved before and after the event. Therefore,
we represent a prepared beam of particles hitting a target as a single
particle hitting another single particle, and whenever this in fact
happens, we observe end products, e.g. in a wire chamber.
Strictly speaking (i.e., in a fuller model of reality), we'd have to
use a multiparticle (statistical mechanics) setting, but this is never
done since it does not give better information and the added
complications are formidable.

As long as we prepare the particles long (compared to the scattering
time) before they scatter and observe them long enough afterwards,
they behave essentially as in and out states, respectively.
(They are not quite free, because of the electromagnetic self-field
they generate, this gives rise to the infrared problem in quantum
electrodynamics and can be corrected by using coherent states.)
The preparation and detection of the particles is outside this model,
since it would produce only minute corrections to the scattering event.
But to treat it would require to increase the system to include source
and detector, which makes the problem completely different.

Therefore at the level appropriate to a scattering event, the 'real'
real particles are modeled by 'mathematical' in/out states, which
therefore are also called 'real'. On the other hand, 'mathematical'
virtual particles have nothing to do with observations, hence have no
counterpart in reality; therefore they are called 'virtual'."

And

"Virtual particles are an artifact of perturbation theory that
give an intuitive (but if taken too far, misleading) interpretation
for Feynman diagrams. More precisely, a virtual photon, say,
is an internal photon line in one of the Feynman diagrams. But there
is nothing real associated with it. Detectable photons are never
virtual, but always real, 'dressed' photons.

Virtual particles, and the Feynman diagrams they appear in,
are just a visual tool of keeping track of the different terms
in a formal expansion of scattering amplitudes into multi-dimensional
integrals involving multiple propaators - the momenta of the virtual
particles represent the integration variables.
They have no meaning at all outside these integrals.
They get out of mathematical existence once one changes the
formula for computing a scattering amplitude.

Therefore virtual particles are essentially analogous to virtual
integers k obtained by computing
  log(1-x) = sum_k x^k/k
by expansion into a Taylor series. Since we can compute the
logarithm in many other ways, it is ridiculous to attach to
k any intrinsic meaning. But ...

... in QFT, we have no good ways to compute scattering amplitudes
without at least some form of expansion (unless we only use the
lowest order of some approximation method), which makes
virtual particles look a little more real. But the analogy
to the Taylor series shows that it's best not to look at them
that way."

By Arnold. Neumaier How real are 'virtual particles'?
 

The Naked Scientists Forum

An essay in futility, too long to read :)
« Reply #424 on: 01/11/2011 08:21:59 »

 

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