They can, just not at the same time. That only applies to fundamental particles though, of course you can still
e.g. be in a house.

I have been thinking about this for a while now, and I do not understand why people claim that two objects cannot occupy the same space. — elucid

As Elucid's comment demonstrates, the answer to your question depends on how you define "the same space." It is always good to define your terms at the beginning of a thread. It's the original poster's job.

I meant two things occupying the same space at the same time.

the answer to your question depends on how you define "the same space."

When saying why can't object A and B occupy the same space at the same time, I meant why can't object A occupy the space occupied by B at the same time.

It seems like bosons might be able to be in the same place at the same time as others.

When saying why can't object A and B occupy the same space at the same time, I meant why can't object A occupy the space occupied by B at the same time. — elucid

It's a fundamental physical law so far as we know. You might as well ask why the speed of light is not a different number. If particles could occupy the same space, the forces acting on them would probably pull them all together, and there'd be no universes, just a black hole.

This is just what we mean be the word "object." If some entities - real or imagined - can be at the same place at the same time, such as fields or ghosts, we don't refer to them as "objects." There is no deep metaphysics here, it's just convention.

↪elucid This is just what we mean be the word "object." If some entities - real or imagined - can be at the same place at the same time, such as fields or ghosts, we don't refer to them as "objects." There is no deep metaphysics here, it's just convention.

I am referring to physical objects.

Present a scenario that shows they can.

↪elucid Present a scenario that shows they can.

I am not trying to argue that they can and I do not know of a scenario which shows that they can.

This is a very interesting question! Coincidentally, I was just thinking about it a few hours ago.

It seems to me that two things in the same place at the same time might be a contradiction. Let me explain. The principle of the identity of indiscernibles given us by Leibniz says that if two things have all the same properties, they can't really be two separate things. They must be the same thing. If two things are in exactly the same place at the same time, aren't they then just one thing? To say that there are two things that are one thing seems a contradiction.

Everything we can say about physical things amounts to some combination of where and when, right?

Some physicists think that everything that can be said about the contents of a region of space can be written on a gridded 2D surface of a sphere of a certain size bounding that region, with each square of the grid having a size of one Planck area. There is a maximum information density for a certain volume of space. And the fundamental unit is the bit, a 0 or a 1. See Bekenstein Bound and Holographic Principle.

Imagine that you are recording information in a grid, and each square can be a 1 or a 0. One square cannot be both a 1 and a 0, can it? Consider Conway's Game of Life, for example. At any given time, a square has only one unique state.

Maybe a way to think about it is that if two things enter into the same region of space at the same time, what you actually have is the sum. It is like adding waves. When two sound waves enter the same space at the same time, they add. They don't remain separate.

So what is confusing you here? People claim that two objects cannot occupy the same space because it doesnt seem as though they can. Pretty simple.

I am referring to physical objects. — elucid

So am I. Physical objects cannot occupy the same space at the same time. Things that can occupy the same space at the same time are not called objects. It's as simple as that.

When saying why can't object A and B occupy the same space at the same time, I meant why can't object A occupy the space occupied by B at the same time. — elucid

As @Echarmion points out - my wife and I occupy the same the same place, my house, at the same time. Three quarks occupy the same place, a proton, at the same time.

So, here are these three quarks. They are pushed apart by the electromagnetic force and held together by the electromagnetic force and the strong force. These forces will be at equilibrium in a stable system. So, how do we get them closer so they can be in the same place? I guess you would have to add a lot of energy. So, let's collide two particles together in an accelerator. What happens then? 1) one, the other, or both can rebound in directions determined by the laws of conservation of momentum and energy 2) one, the other, or both can shatter with the pieces heading off in different directions again based on laws, or 3) they could combine and the combined particle could travel off in a new direction depending on the conservation laws also.

Let's look at possibility 3. Perhaps they will form a new composite particle, e.g two hydrogen nuclei joining to be come a helium nucleus. I don't think this process leads to the particles being what you call "in the same place." What else is there? Can two otherwise indivisible particles somehow overlap with each other? What would be the mechanism for that. What forces would hold them together?

Somebody please correct my physics if it's wrong.

If two things are in exactly the same place at the same time, aren't they then just one thing? To say that there are two things that are one thing seems a contradiction.

Two things being in the same place at the same time does not mean that all their properties are the same. It does not mean that those two things had the same history.

Physical objects cannot occupy the same space at the same time. Things that can occupy the same space at the same time are not called objects. It's as simple as that. — SophistiCat

Fundamental particles can occupy the same space at the same time. See identical particles.

I, at least, consider particles to be physical objects. Here's the conventional usage:

1. A material thing that can be seen and touched.

1.1 Philosophy A thing external to the thinking mind or subject. — Object (Lexico)

Two things being in the same place at the same time does not mean that all their properties are the same. It does not mean that those two things are the same shape, size, were created at the same time or had the same history. — elucid

You mention differences of shape. Let's focus on that for a moment. Suppose we have a 2D world and in this 2D world, we have a square and a triangle "in the same place". Are they truly in the same place? Do they occupy exactly the same space? They don't, do they? I don't care how you size them, there will be places where one is that the other isn't. One point of a triangle, for example, might be beyond the boundary of the square. If two shapes were to perfectly occupy all the same spaces, they'd necessarily have the same shape. You'd have to turn the triangle into a square to get it to perfectly overlap the square. So then you'd have two squares of exactly the same shape in the same place at the same time. Still two different things?

We might have to get into mereology here though. Maybe anything with a shape isn't truly a thing, but rather an arrangement of smaller things. And the smallest things, the true things of which all composites are composed are shapeless. Pick one point that the square and triangle share. This point is just one point. There aren't two points in the same place. If there were, they'd be indiscernible.

Consider a digital image in Photoshop. Superimpose a triangle over a square. Suppose the background is black and the the objects are pure white. 0 and 1. All the pixels where they overlap have a value of 1. All the pixels where just one of them is have a value of 1. All the pixels where neither is have a value of 0. You can't tell the difference between a pixel that belongs to both or to just one. Really, you just have a new shape, possibly no longer a regular polygon.

Suppose instead, we have a range of grey values, representing something like a magnitude of presence for objects. If the triangle has a brightness of 10 and the square 10, where they overlap, we have pixels with a value of 20. We don't have two pixels, each with a value of 10. Rather, we have one pixel with a value of 20. In order to have two pixels, each with a separate value of 10, each with the same coordinates, you'd necessarily need two different images, one for each. The two shapes wouldn't occupy the same spaces. And they wouldn't interact.

That last sentence is key. If two things could overlap and remain perfectly separate like that, they wouldn't be interacting. If they are two completely independent, completely non-interacting systems, how can they be said to be in the same space? What would that even mean?

Fundamental particles can occupy the same space at the same time. See identical particles. — Andrew M

I looked at the link. As far as I can tell with a cursory skim, it doesn't talk about two identical particles being in the same place at the same time while remaining two separate particles. But I don't understand all the physics and math there. Correct me if I am wrong.

What about the Pauli Exclusion Principle? According to Wikipedia:

The Pauli exclusion principle is the quantum mechanical principle which states that two or more identical fermions (particles with half-integer spin) cannot occupy the same quantum state within a quantum system simultaneously.

Consider the addition of waves. Drop a pebble into a pond. Drop another in a different spot. Watch the ripples produce an interference pattern. Can you understand the wave magnitude at any one spot on the water's surface to be two separate values? Are there really two different bits of wave there, moving in different directions?

If two shapes were to perfectly occupy all the same spaces, they'd necessarily have the same shape.

You are right. That still does not mean that two objects occupying the same space share all their properties with each other. By that, I mean that it does not mean the objects have the same history.

That still does not mean that two objects occupying the same space share all their properties with each other. By that, I mean that it does not mean the objects are the same weight, the same color, or have the same history. — elucid

Are you sure? Let's put history aside for a moment. Physically understood, what is weight? What is color? Aren't they both reducible to shape in space and time?

What do you understand this image to depict?



Is this a square and a triangle in the same place?

I have been thinking about this for a while now, and I do not understand why people claim that two objects cannot occupy the same space at the same time. — elucid

Location is an element of identity. If two objects occupy the same place at the same time, they are the same object. It's definitional.

What about dimensionality?

What about dimensionality? — Wallows

Do you mean to suggest that two objects can occupy the same space in two dimensions while being separated in a third? Like a sheet of paper stacked on top of another? In that case, clearly they wouldn't be occupying the same space.

Are you sure? Let's put history aside for a moment. Physically understood, what is weight? What is color? Aren't they both reducible to shape in space and time?

Even if that is true, we cannot put history aside. History of something is its property. Two things, even if the same size, color, weight, shape and in the same location, are not the same things if they have different history.

Is this a square and a triangle in the same place?

The shape of the red dot cumulatively is a square and the blue ones is a triangle, but I would not say that a squared shaped thing is occupying the same space that the triangular one is.

Before we get into the history of things, I want to get more clear on what it means for something to be a thing or an object. When you speak of two things, each with its own history, would a carrot qualify? What about a cloud?

Yes, but that only be asserted from a God's eye view. So, in a Hilbert space of n->oo how can we assert such things?

The principle of identity of indiscernibles says that if two objects are the same in EVERY way, then they must be one thing, not two. So if two things are different in any way, even if it is a difference in location along some spatial dimension not readily known or seen by humans, it IS nevertheless a difference in location in some space, and we can treat the two things as in some way distinct. It doesn't matter if we are talking about Hilbert spaces, with which most people are not familiar, or one of the familiar three spatial dimensions.

Physical objects cannot occupy the same space at the same time. — SophistiCat

They do at the center of a black hole, don't they? Time stops, so I don't know if "same time" means anything there.

I understand that. But, in a world where higher order dimensions influence lower dimensions in a manner of totality, then we can't reach conclusions about things existing in the same or distinct manner, I think.