Can two electrons have the same location?

I don't think modern physics has a logically coherent enough definition of electron to answer this. Consider:

According to Einstein energy has mass. The electric field of an electron is a type of energy and contributes to its mass. Physics says that the strength of the field decreases with the square of the distance. That means the field continues indefinitely far, though it's extremely weak at far distances. So a single electron is technically present in the entire universe, since its field is, and its field is part of the electron.

But what is true for one electron is true for others. So every electron occupies the whole of the universe simultaneously.

However, field theory says that when two electric fields overlap, they modify each other by means of the wave interference effect.

Because "two electrons" simultaneously occupy the same space and co-determine each other, it isn't logically consistent to talk about "two" electrons.

You don't have the slightest understanding of modern physics.

Modern physics has enough understanding of the electron to build the computer that you are using to read this. It is perfectly "logically coherent". When you get to the point where you understand how this works... you will understand how silly your post is.

If an electron occupies all space, then is it wrong to speak of an electron as having location?

I'm guessing I totally misunderstood what a singularity is. It's not that a bunch of stuff has a single location. It's something else. What?

For anyone interested in the science... this is a pretty good layman's explanation.

http://faculty.wcas.northwestern.edu/~infocom/The%20Website/plates/Plate%201.html

If you were to take a class on Quantum Mechanics (which anyone is free to do) you would learn that the theory is very well developed, and explains the behavior of electrons in experiments very well. The science behind this is complex... but it is very well understood... as I pointed out in my previous post, the chips that run your computer (and the internet) rely on this science.

Quantum Mechanics is largely based on this equation (called the Schrodinger equation). If you understand this equation, it will go a long way to give you a real understanding of how electrons work.



Pretending to have any real understanding of modern physics without having studied this equation is fantasy.

Note that maxdancona doesn't address any substantive point I made. Nor does he explain why anything I said is incorrect. He simply seems to be threatened and frustrated, and resorts to personal insults. I think the troll icon he uses is highly appropriate.

I've discovered that I can make all his posts disappear by putting him on an "ignore" list. Yay!

What substantive point have you made?

It seems clear to me that you haven't taken any physics classes, and have instead taken a bunch of hodgepodge science terms together to make random sentences. There are no substantive points... or even non-substantive points here... as far as I can see.

Having a thread tagged science, where two people completely ignore science, is a little frustrating. I just want to make sure that anyone reading this knows that this thread has nothing to do with real science.

Neither vague, handwaving references to Schrodinger's equation nor the essay linked to refute, or even address, the points I raised.

I'll have to add maxdancona to my ignore list. This is the second time he has wasted my time with contentious nonsense.

In physics, it's the point at which formulas break down and become incoherent. When the calculations you rely on tell you that the "answer" is infinity (or infinite)--which is incoherent.

At least that's my understanding.

It's my understanding that electrons are more of a probability field/cloud than an actual point object. And if that's the case, then your question can't even be applied.

I don't see how one can (with logical consistency) speak of "an" electron, much less its "location".

The question of location is actually a very deep one. It includes fundamental problems in physics and mathematics but it is actually a problem of logic.

Physics is full of problems like this. For example, take an object (call it X). X is at rest for every instant of time up to, but not including midnight. Midnight is the first instant that X is moving.

At midnight, where is X?

X cannot be where it was when it was at rest, because it is moving.

If X is somewhere else, how did it get there (and when did it have the opportunity to get there)?

How can X be moving if it hasn't moved?

"Moving" implies changing position.

A mathematician would probably say that at midnight X is exactly where it was when at rest (before midnight), but that its differential acceleration is no longer zero. This is just another logical inconsistency, a way of attaching a mathematical label associated with motion to an object whose position hasn't changed.

The essential problem of location (or position) is one of delineating borders. One must define the border between an object and everything else (not that object).

A border of positive width isn't a real border because it can be subdivided; for example, my skin isn't a good border between my body and what's outside my body, because my skin has width. One might prefer to call the surface of my skin the border, but how does one define this surface?

In order to see that it's a logical problem and to eliminate complications related to the microscopic or atomic structure of skin, we can instead consider an ideal sphere.

Because borders cannot have positive width, the only alternative is no width at all. Indeed, a mathematical surface has no thickness. It is constructed of geometric points. This is the ultimate basis for all mathematical borders: the problem of border divisibility can only be eliminated by introducing something that cannot be divided.

Why can't a geometric point be divided? Because it has no extension in any dimension (direction). But then it does not occupy space, so how can it indicate position in space? A line of a given length has exactly the same length after you remove the end points, because points don't have length. This should make it abundantly clear that a point is a nothing posing as a something. It is in fact a logical contradiction.

I would suggest to PuzzledPerson that he take Calculus 101. That would help him with the basic concepts about mathematics that he is missing (actually a high school pre-calculus class that covered limits would probably do the trick).

However, he is ignoring me because he doesn't want anyone to discuss actual science. Such a shame.

Not to be flippant, but doesn't pretty much everything in physics break down?

The very model object of matter, the atom, appears to be a perpetual motion device: force is required to keep particles of opposite charge (electrons and protons) separated yet bound together in "orbits", yet atoms never run down: the electric force remains potent. If they get the energy from somewhere else (say, the so-called vacuum field), where does that something else get its energy from? Doesn't this lead to an infinite regress? How can "conservation of energy in a closed system" apply if there is no such thing as a closed system, or if potential energy is unlimited?

So far as I can see, physics breaks down at the borders, at the base, and at practically every intermediate step.

Physics is an elaborate "explanation" for things whose rococo detail distracts from and disguises fundamental inadequacies. It's a castle in the clouds resting on the Big Bang: but what does the latter rest on? I guess it's "turtles all the way down", as the whimsical description of Hindu cosmology has it.

Circular definitions, contradictory premises, ill-defined vagueries, infinite regresses, and foundationless arguments, are what physics is based on. Whenever anyone attempts to point out fundamental logical problems, the problems are ignored and dismissed with "it works". Well, gee, so does a dream world in a dream. Until it doesn't. Or until you wake up and realize what befuddled nonsense you were deluded by.

Don't ask me what to replace it with: I may be lucidly dreaming (to a limited extent) but I haven't woken up.

No, I don't think so. "Physics" is a very broad subject which consists of far more than the fantastic metaphysical "explanations" which you encounter in particle physics, cosmology, string theory, and the like.

At one time math was used to encapsulate the essence of relationships derived from empirical observation, and physics itself pretty much devoted itself to the task of "describing the world." Math was the servant of observation.

Early in the 20th century the relationship between math and observation started reversing itself. Math was deemed to tell you what the world was about, instead of "the facts" telling you what mathematical formulas were required to explain it.

Rather than math being the servant of physics, physics is now slave to the math, at least in areas where direct observation is not available.

Maxdancona is, of course, completely correct in all respects. Why people think they can do physics without taking a physics class is a mystery to me. Yes, understanding the Schrodinger equation is an absolute minimum prerequisite to discuss this question intelligently. I had several quantum mechanics classes in college, but it was 40-45 years ago and, unfortunately, I have forgotten all but the highlights. However, my impression is that two electrons can occupy approximately the same location but not exactly the same location. I wouldn't swear to it, though. And yes, you can know the exact location of an electron, although you would then know nothing about its momentum.

puzzledperson's post is sheer nonsense. People learn this kind of stuff in high school physics all around the world. If X is at rest and starts moving at midnight, then at midnight, its position is unchanged and its velocity is unchanged, but it now has a non-zero acceleration.

If that's what they learn, then they should get the hell out of public schools.

Spoken like someone who has never taken a physics class. This has been well understood since Newton's time.

Great. Explain it.

At some point in time, an object begins to accelerate from rest. In that exact instant, it has an acceleration (by definition), but when zero time has elapsed since the acceleration began, it does not yet have a changed velocity or position.

If v is velocity and s is displacement:

v = at
s = 1/2 a t^2

At t=0, both of these are still zero. An instant after t=0, the object will have both non-zero velocity and non-zero displacement from its original position, but not at t=0.