What Happens When Point-Like Particles Interact?

[glengarry]

So much hay is made out of the fact that quantum theory—and its associated experiments—violates the principle of local causality, as canonically developed by the classical (Newtonian) and relativistic (Einsteinian) models. But no one ever really asks about what these models are 'truly' saying about physical reality. That is, in all of these theories, it is axiomatically assumed that material bodies, in the elemental sense, come in the forms of geometric points. But there is a major difference between the following two ideas:

1) points as the solutions to linear, analytical equations
2) points as 'really existing' physical objects

In fact, it is my thesis that the desire to satisfy idea #1—at least within the community of mainstream academic physics—has always overshadowed the question that idea #2 is constantly begging. And this question is:

"If the form of physical bodies, in the most elementary sense, is not that of the geometric point, then what is it?"

But before we even demand from ourselves a [hypothetical] answer to this question, let us return to the original question: How is local causality possible?

That is, we will assume the existence of two elementary bodies that come in the form of geometric points, and for the sake of simplicity, we will consider a one-dimensional space. Now, just like those 'cars approaching each other from opposite directions' questions, we will consider our particles, A and B, to be involved in the same kind of collision course.

So A and B are now approaching each other with some arbitrary relative speed (it makes no difference what the individual velocities might be in a given frame of reference). So, A and B get closer and closer until something happens. My question is simply this:

"What is the nature of this 'something' when we say that two physical bodies, in the form of points, have 'interacted'?"

And I ask this because of this difficulty: the only way that we can say that two points are not different is when they are, in fact, the same point. So here are the choices that we have left:

1) The two points are not interacting precisely because they are different—i.e. there is some amount of space between them.
2) It is senseless to say that interaction exists precisely because there is only a single point in existence.

Anybody have any comments about this difficulty?

 

[haael]

"If the form of physical bodies, in the most elementary sense, is not that of the geometric point, then what is it?"

Probability density. There are fields in spacetime which have some value. From these fields you can derive position, mass and other properties of what we call particles. Value of the fields itself appears to us as the probability of finding a particle at specific point.

I strongly believe that the spacetime itself is composed of points. In other words: it is Riemann manifold and position operators do exist and commute. However, we don't know what future theories would be. Maybe they will not have concept of spacetime points, i.e. the spacetime would be quantized or position operators would not commute.

"What is the nature of this 'something' when we say that two physical bodies, in the form of points, have 'interacted'?"

All classical theories have one common drawback: they assume that particle count is constant. No classical theory can explain how particles annihilate, pop up or change. So it is impossible to tell this using only concept of point.

In quantum physics, however one field can continuously transform into some another.
Suppose we have two fields: "a" and "b". In the beginning, field "a" has probability 1 and "b" is 0. Then, the probability of "a" starts to decrease and "b" goes up, so that the sum of probabilities remains 1.

There is no one moment of "interaction". It's just high possibility of seeing substrates before "collision" and high chance of seeing products after. You can say that probability flows from one field to another.

 

[glengarry]

Okay, those are some good, textbook answers. However, I was asking about the form of physical bodies and not of spacetime. Your reply was:

"I strongly believe that the spacetime itself is composed of points."

Are you saying that 'physical bodies' and 'spacetime' are one and the same concept?

 

[ansgar]

define "physical"... you will see that this is ambiguous

 

[glengarry]

Good point, ansgar. The conclusion being that the discipline known as 'physics' is ambiguous. Should we attempt to set the record straight here and now?

 

[ansgar]

Good point, ansgar. The conclusion being that the discipline known as 'physics' is ambiguous. Should we attempt to set the record straight here and now?

You brought it up, what do you mean by "physical"?

 

[haael]

Are you saying that 'physical bodies' and 'spacetime' are one and the same concept?

I was not saying this here, but indeed, I do believe that spacetime and matter is the same thing.

I was asking about the form of physical bodies

"Physical body" is an illusion that we mere humans see when we dare to look at quantum fields. Quantum fields are defined on (I believe) absolute space. Then math follows.

 

[glengarry]

You brought it up, what do you mean by "physical"?

I guess this definition off of the top of my head would suffice:

"Of or related to the objects of experience"

Satisfied?

 

[glengarry]

There is no one moment of "interaction". It's just high possibility of seeing substrates before "collision" and high chance of seeing products after. You can say that probability flows from one field to another.

My main concern with theoretical physics is with 'scare quotey' language just like this. On the one hand, we want to use (i.e. be inspired by) certain images that are related to our every day experiences (e.g. watching an apple fall from a tree).

But when pressed, the typical theoretical physicist will say that these are only analogies, and that the formalism is the thing that really counts. What I want is to come up with an idea of theoretical physics that no longer plays such games.

Can anyone help me?

 

[ansgar]

I guess this definition off of the top of my head would suffice:

"Of or related to the objects of experience"

Satisfied?

my experience and all data suggest that there are point particles preserving local causality..

What are you really after?

are you a curious physics student? a professional physicists or physics layman?

There are many people out there having hard to comprehend the concept of "points"

 

[haael]

Can anyone help me?

I am helping you. You just yet have to accept it.

By "interaction" and "collision" enclosed in dreaded quotes i meant classical interaction and collision. Classical electron and positon approach, then they classicaly collide, a tiny thunder smites and two photons pop out. This is the classical view of interaction.

In reality, there is no such thing. Quantum interaction (not quoted) is about changing relative probabilites of fields. Also, quantum fields are not point particles, so there is no concept of collision.

If you do not like this view of physical world, it's not my fault. You should however stick to some "realistic" interpretation of QM, which is necessarily non-local.

Reality is about maths, not falling apples. You should not believe that there is a tiny falling apple inside each atom. There are lot of quantum fields, though.

 

[glengarry]

my experience and all data suggest that there are point particles preserving local causality..

Or is it your experience rather that there are three-dimensional bodies that always seem to be where you expect them to be? I guess what I'm really trying to get at is the huge disconnect between this kind of everyday experience and the theoretical difficulty that I presented in the first post.

What are you really after?

Ah... 'reality.' That's a tough one!

are you a curious physics student? a professional physicists or physics layman?

None of the above, but we can get to that in due time!

 

[DrChinese]

But when pressed, the typical theoretical physicist will say that these are only analogies, and that the formalism is the thing that really counts. What I want is to come up with an idea of theoretical physics that no longer plays such games.

Me too! I want to stop these games. Gimme something I can touch.

And after the physicists, let's go after the philosophers!

 

[ansgar]

I am helping you. You just yet have to accept it.

By "interaction" and "collision" enclosed in dreaded quotes i meant classical interaction and collision. Classical electron and positon approach, then they classicaly collide, a tiny thunder smites and two photons pop out. This is the classical view of interaction.

In reality, there is no such thing. Quantum interaction (not quoted) is about changing relative probabilites of fields. Also, quantum fields are not point particles, so there is no concept of collision.

If you do not like this view of physical world, it's not my fault. You should however stick to some "realistic" interpretation of QM, which is necessarily non-local.

Reality is about maths, not falling apples. You should not believe that there is a tiny falling apple inside each atom. There are lot of quantum fields, though.

well, one should be more modest.. Quantum Fields are "just" theory/model... but everything else in your post is fine.

 

[haael]

Quantum Fields are "just" theory/model...

A model far more closer to reality than the concept of solid point-like particles everyone in this world has printed into his head before birth.

 

[ansgar]

Or is it your experience rather that there are three-dimensional bodies that always seem to be where you expect them to be? I guess what I'm really trying to get at is the huge disconnect between this kind of everyday experience and the theoretical difficulty that I presented in the first post.

welcome to the world of QM... and special relativity, which is not taking place at everyday life basis hence our brains have no intuitive sense for such phenomenon except for what we can deduce from our logical and analytical "brain-spot" (i.e. making up theories based on math and ways to test them)

why should even human beings be able to understand reality as "it is" in the first place, what kind of premise is that?

You seem to limit yourself quite a bit if you want to feel everything.. have you ever felt the moon by your hands? have you felt a single atom? have to touched a galaxy? once? maybe twice?

Why should theoretical physics adapt to you? The reason for why choosing maths to formulate science is that it is unambiguous!

 

[ansgar]

A model far more closer to reality than the concept of solid point-like particles everyone in this world has printed into his head before birth.

well maybe, the more modest and humble answer would be that QFT fits to data over a larger range of energy scales than other models.

 

[ansgar]

I should probably stress that it is a difference in trying to DESCRIBE reality and KNOWING what reality is. The first task is physicists task, the other one touches upon methaphysics.. which is NOT the forum we are at this very moment..

 

[glengarry]

I am helping you. You just yet have to accept it.

Yes, you are helping, and I am accepting your help. I'm just trying to understand, is all.

By "interaction" and "collision" enclosed in dreaded quotes i meant classical interaction and collision. Classical electron and positon approach, then they classicaly collide, a tiny thunder smites and two photons pop out. This is the classical view of interaction.

My point in the OP is that there is no such thing as a theoretically complete notion of classical locally-caused interaction.

In reality, there is no such thing. Quantum interaction (not quoted) is about changing relative probabilites of fields. Also, quantum fields are not point particles, so there is no concept of collision.

If you can't provide a good definition of classical interaction, then I don't know what I'm supposed to make of the idea of quantum interaction. That is, the very concept of interaction (i.e. causality) is what is at issue.

If you do not like this view of physical world, it's not my fault. You should however stick to some "realistic" interpretation of QM, which is necessarily non-local.

My point is that QM, in its purely formal understanding, has nothing to do with a "view of [the] physical world." That is, nothing is being viewed. It's pure mathematics, and we should stop speaking of it as if there is a connection to physical reality.

Reality is about maths, not falling apples. You should not believe that there is a tiny falling apple inside each atom. There are lot of quantum fields, though.

What I'm trying to say is that 'reality is just reality' and 'mathematics is just mathematics.' In my view, the question that theoretical physics should come to grips with is the way in which these distinct concepts can possibly relate to one another.

 

[glengarry]

Me too! I want to stop these games. Gimme something I can touch.

And after the physicists, let's go after the philosophers!

You can touch a Riemannian manifold.

 

[glengarry]

I should probably stress that it is a difference in trying to DESCRIBE reality and KNOWING what reality is. The first task is physicists task, the other one touches upon methaphysics.. which is NOT the forum we are at this very moment..

No, many theoretical physicsts would say that even the term 'description' is too strong. That is, according to the standard, Bohr/Bell notion of QM, the only thing involved is the prediction of the results of a given experimental arrangement over an infinite number of trials.

 

[haael]

My point in the OP is that there is no such thing as a theoretically complete notion of classical locally-caused interaction.

Yeah, there is not.

That is, the very concept of interaction (i.e. causality) is what is at issue.

Locality and causality on a quantum level come from the fact that the probability current may not flow as it wants, but must obey some laws.
Imagine quantum fields as some kind of gas or liquid. This liquid may not disappear, appear out of nowhere and it must satisfy local continuity. From this law come some observed facts, i.e. that nothing can travel faster than light, bodies can not suddenly disappear and apples fall from trees.

Is this what you wanted to understand?

It's pure mathematics, and we should stop speaking of it as if there is a connection to physical reality.

What I'm trying to say is that 'reality is just reality' and 'mathematics is just mathematics.'

No, mathematics is the reality. What we see with our eyes is not. If maths says something you think is wrong, then you are wrong, not maths.

Quantum physics is connected to real world. Our senses are not, they are just tricks the evolution gave to chimps so they can eat more bananas. Maths is our only way to explore reality, even if it gives us answers an average chimp would not believe.

 

[glengarry]

welcome to the world of QM... and special relativity, which is not taking place at everyday life basis hence our brains have no intuitive sense for such phenomenon except for what we can deduce from our logical and analytical "brain-spot" (i.e. making up theories based on math and ways to test them)

Why would one need a "way to test a theory"? Isn't a theory supposed to be the proof of those empirical observations that are otherwise just going to remain random collections of "events"?

why should even human beings be able to understand reality as "it is" in the first place, what kind of premise is that?

Hmm... ask the first guys in ancient Greece why they started pondering in such ways, only to infect us all, two-plus millenia later with that damn virus that is known as "trying to understand reality"!

You seem to limit yourself quite a bit if you want to feel everything.. have you ever felt the moon by your hands? have you felt a single atom? have to touched a galaxy? once? maybe twice?

Is there any difference between feeling the moon and being affected by its gravitational pull? Why must we always reduce things to the base sensation of touch?

Why should theoretical physics adapt to you? The reason for why choosing maths to formulate science is that it is unambiguous!

Do you know how many mathematicians would disagree with that statement? It is true, that to non-mathematicians, everything that mathematicians devise/prove is carved in stone. But let me assure you, there is a huge amount of interpretation that goes on in that field!

 

[glengarry]

No, mathematics is the reality. What we see with our eyes is not. If maths says something you think is wrong, then you are wrong, not maths.

How about we just put it like this:

Mathematics deals with mathematical reality and physics deals with physical reality. I think that the project of theoretical physics is to find a way to marry these two forms of reality. To me, no one has been very successful in showing how these two realities are related. I think it is a very interesting question.

 

[haael]

Mathematics deals with mathematical reality and physics deals with physical reality.

Physical reality is a subset of mathematical reality.

I think that the project of theoretical physics is to find a way to marry these two forms of reality. To me, no one has been very successful in showing how these two realities are related.

What you are calling (physical) reality here is just an illusion created by your senses. Quantum physics describe true physical reality. And why can you not relate physical reality with what you see? The answer is simple: your mind is fooling you. No further explanation needed.

Now, forget that the world is what you see with your eyes. Wake up from Matrix. Maths is the only true world and it always was.

 

[glengarry]

Quantum physics describe true physical reality.

This statement just shows how "off the mark" you are in terms of how the typical theoretical physicist understands the nature of his/her own profession.

Now, forget that the world is what you see with your eyes. Wake up from Matrix. Maths is the only true world and it always was.

Trust me, I understand the sentiment in this statement entirely. I mean, Neo's got nothing on me, when it comes to how I feel about the "real world" at times.

But I think that there is a delicate balancing act that is always in order, as long we want to remain "relevant" voices within the pantheon of intellectual discourse.

You see, there is the world of sensation that exists right in front of my eyes, and that is just the thing that fascinates me to no end (e.g. puppies, girls, computers, etc...). And if this world did not exist, then there would be nothing to which mathematics could possible apply.

But at the same time, there is also a world that exists entirely within my mind that consists of things like circles, square, parabolas, the number 42, and suchlike.

What we have, then, are these two things, that, for all intents and purposes, are totally at odds with each other:

1) Physical objects that can be sensed
2) Mathematical objects that can be understood

Now, the goal of theoretical physics, seems to me to be that particularly unfortunate science that tries to figure out how physical objects can be understood!

 

[haael]

This statement just shows how "off the mark" you are in terms of how the typical theoretical physicist understands the nature of his/her own profession.

Physics is not my profession, to be honest. I'm a mere computer scientist. Believe me, computers have even less to do with common logic than quantum physics :).

You see, there is the world of sensation that exists right in front of my eyes, and that is just the thing that fascinates me to no end (e.g. puppies, girls, computers, etc...). And if this world did not exist, then there would be nothing to which mathematics could possible apply.

No, puppies and girls exist, because maths allows them to. Maths could as well exist on its own. We should be thankful to her, that she created our Universe and us humans in particular, perhaps out of boredom. Now, our life task is to explore her, preferably for eternity.

But at the same time, there is also a world that exists entirely within my mind that consists of things like circles, square, parabolas, the number 42, and suchlike.

Good thing that you distinguish what is real and what is in your mind, but you are mistaken in some things.

There is some real world. You and me live in it. Now, we postulate theories about it. One such theory is called "common sense" and it seems we all have it hard-wired in our heads by evolution. It is a nice theory, since it allowed us to last for few million years as a species. But when we tie to it too strongly, the problems begin.

One axiom of common sense is that there are solid "things" that are localized in space. When you put an apple to a hat, the apple is in the hat. You can pull it out then.
But what happens when you want to apply this axiom to double-slit experiment? Where is the electron? Common sense tells you, that an electron, as any other solid thing, should have its position. But this is inconsistent with what we can see with our own eyes.

The uncomfortable truth is, that common sense is not a perfect theory. It is simply in contradiction with the Reality, the real mathematical structure that constitutes our world.
So, we are forced to throw out the common sense and replace it with more sound theory, namely quantum physics. It is a better theory, since it can explain existence of puppies, girls and diffraction pattern on double-slit experiment.
The world exists. It's just the assumptions we make on it are often false.

I know how you feel, because I once felt the same. I found a contradiction between my common sense and reality, which was painful, since I always believed that common sense is equivalent to reality. However, after you will have made that step, you will fill better.

There is no such thing as a solid object with the position. There are only quantum fields. Accept the facts.

1) Physical objects that can be sensed
2) Mathematical objects that can be understood

Now, the goal of theoretical physics, seems to me to be that particularly unfortunate science that tries to figure out how physical objects can be understood!

Nothing can be sensed, except few illusions in my head. However, sensations are reflections of true reality, so we create physics so that they make sense :). Physics is a better theory of reality than common sense, since it has fewer contradictions.

Plus, physical objects are special case of mathematical objects, so they can be understood.

Oh God, I'm struck with Plato philosophy. Someone help me.

 

[glengarry]

Now I want to get back to my whole point for this thread...

So many of the difficulties that arise in discussions of physics are the result of intermixing the worlds of sense and reason. And it is precisely when this kind of intermixing occurs that heads or tails cannot be made out of our physical theories. That is, they become subjected to that word that is the bane of all theoreticians, alive or dead: INTERPRETATION.

The problem is just the following. When we are born, we have all of these wild and crazy experiences with the world, as it is immediately perceived. As we grow older, however, things seem to become more organized because many of our experiences tend to repeat themselves over, and over, and over...

In my opinion, theoretical physicists are just those people who are trying to explain why it is that the most common phenomena (i.e. gravity, magnetism, light) behave so predictably. So they construct mathematically ideal models and then test these models through thought experiments. And it is precisely those models that have successfully passed the rigors of the "thought experiment tests" that are taken to be accepted theories.

The difficulty arises, however, when we have all of these empirical physicists, watching from the sidelines, who have nothing to do but twiddle their thumbs while all of this is happening. So, they want to construct "real" experiments that are meant to approximate the ideal experiments in order to test if the already proven theories are, in fact, true.

And theoretical physicists have never tried to hinder the empiricists from doing what they do, because to do so would be to open themselves up to critisicm from a "naive" public that holds on to the antiquated notion that "ideal" scientific theories are things that are always subject to being proven by "real" experimentation.

But there is a vicous cycle in this kind of thinking. That is, the only reason why theoreticians are theoreticians is because they are interested in fully comprehending (whatever that means) those basic kinds of phenomena that are all too predictable. The only kind of "proving ground" that even makes sense in this situation is just that very organ that exists between our ears.

My goal is to align myself with a group of thinkers who are wholly and completely unapologetic when it comes to this idea: What they have proven is indeed the case, unless and until someone else can prove why the proof in question is flawed. This, after all, is the selfsame notion as the mathematical theorem.

I'm interested in finding people who want to drop all of the pretenses that physical theories can ever somehow be lacking "real" proof. It's all so much nonsense, and in my opinion, the sooner it all dies a violent death, the better.

 

[glengarry]

No, puppies and girls exist, because maths allows them to. Maths could as well exist on its own. We should be thankful to her, that she created our Universe and us humans in particular, perhaps out of boredom. Now, our life task is to explore her, preferably for eternity.

These notions are nothing other than the kind of dogmatic, religious propositions that have precisely no place in forums like these. But seeing as I am not a moderator, feel free to throw them around until your heart is content :)

Oh God, I'm struck with Plato philosophy. Someone help me.

This also shows how "off the mark" you are about philosophy, too, because Platonic thought is diametrically opposed to the notion that:

Physical reality is a subset of mathematical reality.

 

[haael]

These notions are nothing other than the kind of dogmatic, religious propositions that have precisely no place in forums like these. But seeing as I am not a moderator, feel free to throw them around until your heart is content :)

The proposition that the world is not mathematical is a metaphysical dogma as well. God, even the statement that empirical science leads us to truth is a dogma.

We have to accept some dogmas first, before we start to make science. The assumption that the world is logical/mathematical is a really good one.

Physical reality is a subset of mathematical reality.

If Plato lived today, he would definitely say so.