Two Objects Occupying the Same Space
Hi everyone,
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.
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.
Comments (77)
e.g. be in a house.
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.
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'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.
I am referring to physical objects.
I am not trying to argue that they can and I do not know of a scenario which shows that they can.
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.
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.
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.
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.
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:
Quoting Object (Lexico)
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?
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:
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.
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?
Is this a square and a triangle in the same place?
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.
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.
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.
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.
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.
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.
I don't follow. Can you lay your thinking out a little more clearly?
Have you read the book: Flatland?
Yes.
So, the same logic at play just for us existing in a progressive flow of the fourth dimension being time...?
Describe the situation you are imagining, including all of the dimensions, even the ones we can't see.
Well think of a camera taking a timelapse photo of a flower. The colors are changing but the object exists spatially in the same place? I'm on my phone so sorry for the crappy posts.
The point in this thread has been the question of whether two truly distinct things can be in the same place at the same time while remaining distinct. I don't see how the flower fits this. Explain.
I was more leaning towards the point of the colors changing wrt. to the timelapse photo of the flower. Does that clarify anything?
As does space. Gravitational singularities - the center of black holes - are currently either considered to be volumeless or unknowable in terms of space. Its part of the spacetime paradigm, from which gravitational singularities were first predicted.
At any rate, it's understood that there are no separate objects at the center of black holes. The vacuum field comes to mind, but even then, there wouldn't be individual particles in gravitational singularities - this from everything I've read up on. Their spatiotemporal location is determined by surrounding givens that are spatiotemporal.
Fine. Two fields can occupy the same space. How's that?
You’re talking about the experience of an entity: its fifth dimensional aspect. With the same size, colour, weight, shape and in the same location in spacetime, two ‘things’ that reach this point coincidentally from different trajectories not only have different histories, but may have different futures, as well. When measured or observed in spacetime, they cannot be distinguished from each other in that moment, and would be the same ‘thing’ to an observer.
But from a five-dimensional awareness, they are two separate entities because we are aware of their different history. So even if they combine in that moment and become one physical ‘object’, the fact that we knew them to be separate prior doesn’t just vanish, but becomes a complex history of the object in the experience of the fifth-dimensional observer. Without this fifth-dimensional awareness of history, any observation of the two objects would merely relate three-dimensional spatial location changes to different points in time (the fourth dimension). When all of these are identical, there would be no way to distinguish between the two ‘objects’ at the point of observation/measurement.
:grin: Fields of what?
Na, I'm in general agreement with @petrichor on this one. Were two fields to occupy the exact same space at the exact same time, they'd be one and the same field. Edit: For greater precision: this for that span of time in which the exact same space is occupied, even if this now singular object is in some way a type of hybrid of it's previously two or more parent objects.
Why would we think of them as the same field?
Your flower is one object in different states at different times. That's not what we are talking about in this thread.
Temp and pressure relate by way of volume. They only track with a constant volume.
A temperature field is not the same thing as an electromagnetic field, though they occupy the same space.
So then I'll ask: if a temperature field and an electromagnetic field occupy the exact same space at the exact same time, in which way are they two different physical givens? (Rather than being two ways of appraising the same physical given.)
There is no such physical thing as a temperature field.
As for such things as the EM field:
https://en.m.wikipedia.org/wiki/Grand_Unified_Theory
Cool. What kind of object is a temperature field?
Wanted to add that they also relate by way of causation, specifically they (to the extent they are considered different) bidirectionally cause each other. But this can get into tricky issues, I think.
Quoting frank
A conceptual object?
I think you mean abstract object. A number is an abstract object. Is that what temperature fields are?
Yea, abstractions we're aware of are conceptual to us.
Quoting frank
Well, you're the one who brought up temperature fields. I was only using temperature and pressure as an analogy. I thought you'd know what they are when bringing them up.
More soberly, temperature - as in cold and hot - is a cognitive abstraction relative to the particular makeup of lifeforms. Scientific models of temperature are entwined with our cognitive abstractions of cold and hot. But this bring the conversation into fields far removed from that of the thread.
There's no clear cut answer. Whether a temperature field is a physical or abstract object (it's certainly not a mental object) is a philosophical question.
Consider a population density map. It is sort of like a field. But is there any real thing out there that is a population field? No. There are just individual humans arranged in various concentrations. Temperature is the same sort of thing. What is temperature? It is motion in atoms. When you understand it this way, you see that there is no actual temperature field. Modeling it at a high level as a field might be useful, but for metaphysical discussions like this, we need to be sure we are talking about the real things that actually exist out there, not just the convenient ways we think about things in high-level models.
https://en.m.wikipedia.org/wiki/Kinetic_theory_of_gases
The EM field is probably also just a feature of models we use. In a grand unified field theory, we reduce everything to one. And that's very likely to be the correct picture.
It's considered by physicists to be a physical object. Do you disagree with them?
I'll link again to this:
https://en.wikipedia.org/wiki/Grand_Unified_Theory
This is the direction in which physics proceeds. Things once thought distinct are shown to be one thing. Einstein famously showed equivalence of mass and energy. Maxwell earlier showed the magnetic and electric fields to be one thing.
We model things at different levels. Sometimes, as with something like geopolitics, modeling it all in terms of the lowest-level particle interactions would be unwieldy. So we use higher-level abstractions, such as "nations" and "regions" and "strategic interests".
You could have a map showing crime density and another showing poverty and another showing disease rates. You could then say that the crime field and the poverty field and the disease field are three things occupying the same space. But that would mean misunderstanding what these are. They aren't physical things. Going down to lower levels, it is revealed that crime and disease and whatnot are all reducible to the way particles are arranged in space and time.
Consider a pile of clay cubes and a clay dinosaur. They seem like different things at a high level. But if we ask what they are at a more basic level, they are both just different forms of clay. And if we compare clay to wax, we see that they are actually different ways of arranging the same basic stuff. And this continues until it is all just different arrangements of one underlying substance. And the only real things are the bottom-most fundamental constituents of reality. All the higher-level stuff is just convenient ways of modelling. We mentally carve the world up into objects like dogs and trees because it is useful to do so.
Notice that as we go down to more and more basic things, to smaller and smaller things, there are fewer and fewer different kinds of things. At the level of planets, no two are alike. There are gazillions of ways to arrange matter at that scale. But at the scale of amino acids, there are far fewer unique structures possible. Go down still further and there are fewer still. We can expect that at the bottom, there is just one. And the fact that we see this trend of fewer unique things as we go down suggests strongly that matter is not infinitely divisible. If it were, there'd be an infinite number of ways to arrange matter at any scale. It would be unlikely that we'd see such things as electrons being all the same.
Physics generally proceeds by unification. There is no reason to expect otherwise.
If you are talking about the atoms from one "object" fitting between the atoms in another, you are not actually talking about two actual physical things being in exactly the same place at the same time. Here no two elementary particles are actually in exactly the same place at the same time. It is a situation like my earlier illustration. And if you were to do that, say with two buildings, you wouldn't have anything resembling buildings at the end of it, given all the inter-atomic forces that would be at work.
You might be interested to read this:
https://en.wikipedia.org/wiki/Theory_of_everything
It says that bosons can share the same quantum state (which includes position). Fermions can't share the same quantum state but they can still share the same position if some other property differs (such as spin state).
Note that there are interpretive issues about what position entails given Heisenberg uncertainty. But the general point is that two particles can be indistinguishable in principle and it is this feature that leads to quantum interference effects. For a nice example of this with two particles, see the Hong-Ou-Mandel effect (where the two particles enter the beam splitter at the same time and produce interference effects).
What does it mean, precisely, for two things to be in the same quantum state?
Also, when it comes to interference effects, aren't we just adding waves, like in the example of water ripples I gave earlier? And isn't the wave in this case a probability wave?
Now think of that timelapse as a GIF and you'll see it's layered and not spatially the same.
If two objects occupy the same space, they meld - and become qualities of one object.
You are just making my point. You choose to include elementary particles into things that you call "objects." I don't think it's a conventional use of words, but whatever - the point is that your choice of whether or not to call something an "object" has no metaphysical implications.
Elementary particles are tricky if you want to talk about them being in the same place at the same time. The best you can do is talk about their quantum states and their superpositions. But then you might as well talk about superpositions of classical fields - here at least being in the same place at the same time is well-defined. If you want to call classical fields objects, then of course you will find that such objects can be in the same place at the same time, but again, this is just word manipulation, nothing more.
Quoting Andrew M
That's a different meaning of "object." Sumerian grammar can be an object of a study in this sense.
That's kind of a silly thing to say, on the one hand. A field is "a physical quantity... that has a value for each point in space-time." And temperature is, of course, a physical quantity. One can talk about temperature fields, and electron fields, and all sorts of other physical fields, and they all exist in the same place (all place) at the same time (all time). But they are not physical objects, you would object! Well, yeah, when we talk about physical objects, we usually talk about things like chairs and stuff. So don't call things that are not object-like objects, and you'll get the conclusion that objects cannot be in the same place at the same time. Or do call them objects, and you'll get a different conclusion. Whoop-de-doo.
Have you seen anything to the contrary? Everyone would be surprised, even shocked, if you have.
One piece of evidence that may or may not convince you is solid objects are incompressible. In terms of particles consider an object A composed of 2 particle x and y. If two particles could occupy the same space then we should be able to compress A to the size of an x/y. This isn't possible. I haven't seen it being done.
You may say gases are compressible but that's explained in terms of squeezing out the space between the particles
An interesting fact is liquids are compressible too. Strange because there's more inter-particle space in liquids in gases.
Liquid behavior is interesting because despite the existence of bigger spaces between particles they aren't compressible. It may be that particles, and by extension any object, can occupy the same space but some kind of force, electric repulsion for example, keeps them from doing so.
Therefore, while objects, except gases, at a human scale can't occupy the same space, it may be that that's possible but prevented by inter-particle repulsive force of some kind.
In this discussion, I think the intuitive image that most of us have of what is actually being disputed is whether two pieces of actual physical matter can actually overlap while remaining distinct. As everyone who has taken high-school physics or chemistry knows, a temperature field is an abstraction that represents such things as the average kinetic energy in the particles of a gas at a given point in space. For our purposes though, we are talking about the actual stuff, the particles themselves, not a smeared-out representation of their average kinetic energy.
Maybe some others aren't even thinking about the same problem as I am, in which case we are talking past one another. In my view, if we allow our high-level abstractions to be considered physical objects for the purposes of asking whether two physical objects can overlap, it is trivial to say that two such objects can indeed overlap. Sure, a storm can be in the same place as the sky. A dog can also be in the same place at the same time as a collection of hairs, blood vessels, kidneys, lymph nodes, and so on. Trivial. Carve up the world however you like and name what's inside the boundaries you arbitrarily define whatever you want and then show that some of them overlap. Can urban blight overlap with a sunny day? Sure, why not? Can a wealth-concentration field overlap with a happiness-concentration field? Sure. We can even have another field that represents some relation between wealth and happiness, a happiness-over-wealth field. It might be interesting to see if it varies from region to region.
Personally, I find it interesting to ask about the nature of fields and particles and whatnot. What are we really talking about? Are they real physical things? Or are they abstractions we use to represent things, like temperature fields? Air traffic controllers use little strips of paper to represent airplanes. And their system works well for managing the traffic. But it would be a mistake to take the map for the territory. When we think of a field as a real physical thing, are we taking the map for the territory? I don't know! I would like to know!
And yes, as you seem to have noticed, I don't consider such objects as chairs to be real beyond the way our minds carve up the world. The matter that composes them is real. But there is no true boundary between a chair and a pillow sitting on it that says each is a truly distinct thing. It is like the strips of paper representing airplanes. It would be too much for the air traffic controllers to think about everything involved. So they take a shortcut and used a much-simplified model. That's what all high-level scientific theories do.
But for the purposes of inquiries such as the present one, we need to get as low-level as possible. What is the actual stuff? Is it multiple? When we talk about two fields coexisting in the same place as two separate objects, are we confused? Is it really just two aspects of one more fundamental thing? What about two particles in the same place? What are we talking about, really?
In other words, if we make up some incoherent gobbledygook . . .
A quantum state contains all the information about a quantum system. For two photons to be in the same state means there is no information, in principle, that distinguishes them. Which leaves us with cardinality (i.e., 2 photons) but not individual photon identities.
For why this is significant, consider the Hong–Ou–Mandel experiment again. Suppose the photon entering the beam splitter at the top is named A and the photon entering at the bottom is named B. In state 2, photon A ends up at the bottom and photon B ends ups at the top. Whereas in state 3 photon A remains at the top and photon B remains at the bottom. However according to QM, there is no information that would physically distinguish those two states - they are physically equivalent. So their respective amplitudes add which manifests as destructive interference, as observed. Whereas classical physics (in which those states are physically different) is unable to predict what is observed.
Quoting petrichor
Yes. But it's worth noting we're not observing waves, we're observing particles at specific positions or with specific spins (or whatever we choose to measure).
Yes, but it's motivated by the ordinary definition, not an arbitrary choice. I think the relevant characteristic of objects is that they are concrete things that can be observed or have their properties measured. That's compatible with "a material thing that can be seen and touched".
The question of whether objects can occupy the same space at the same time or not seems to me to be more associated with classical physics rather than something necessarily associated with the term.
"why people claim that two objects cannot occupy the same space at the same time"
What is meant by "objects"? Are they bulky solid things that we can see and touch, as per one common meaning of the word "object"? Or anything to which one can refer, as per the grammatical sense of the word? Or something else?
And what does "cannot" mean in this sentence? Cannot in fact (in our world, to the best of our knowledge)? Or in principle - what principle? If we relax the grip on reality and allow other possible worlds, then we have to have a good grip on the trans-world "objecthood", lest the word loses its meaning.
And what does "why" mean? Are we looking for a reductive explanation in terms of some underlying physics? That would be a relatively easy question to answer. A metaphysical principle? Then we'll have to tangle with objecthood and counterfactuals.
Quoting petrichor
Everything is an abstraction, elementary particles included. Physicalist reductionism - the position that only (some) entities posited by fundamental physics really exist, everything else being mere abstractions and pragmatic simplifications - is a defensible view, but it must not be assumed unconsciously, as a matter of fact.
In that case, the somewhat flippant answer that I gave you in the beginning still fits. There are plenty of things in our ordinary experience that fit this description (and you are not asking "why" such things exist, you take their existence and their properties for granted - which is fine, one has to ground the discussion somewhere). We refer to such things as "objects" in the English language. If we learn about certain entities that do not fit this description, such as rays of light or bosons or spirits, we may accept their existence, but we won't refer to them as "objects" in the same sense in which call chairs "objects." This is just a matter of categorizing and naming things.
So what we're calling a "common" meaning for "object" is actually from an outdated scientific model.
What I wanted to add is that if we are going to ‘conceptually’ tackle the problem of same space/time co-occupation, then it is important we make the argument about any possible entity and make it type agnostic. For what we are concerned with here is the logical possibility of co-occupation by anything that can either be measured, or observed, or detected, or all. Because if the notion of co-occupation is 'possible' say in the case of photons, then it makes it a fact that the notion qua notion is a logical possibility given the entities in question have certain properties which photons would be an example of. So we need to talk in terms of whether it is possible in principle for any number of observable, measurable, or detectable entities to occupy the same space.
The other complication is should we position the question around ‘space/time’ at all? Or should we find a better way to ask the question? Because if we can’t then it either means our conceptual understanding of space is such that it is different from everything else, in which case we need to be able and define it, or it means there is a problem related to our question with the notion of space/time at the heart of the problem.
A related issue is the notion of ‘same’ used in the ‘same space/time location’. We have to be very clear about what this notion means. For example; to say two identical entities could have different histories just begs the question. In possible world W1 we can have two intrinsically identical particles, identical mass, same shape, and so on, where each have been traveling in a straight line for 1 year since they came into being. Our description of their history is the same it seems. Nothing in the description of one is different than the other. We may now wish to track them back to their source of origin and how they came into being. But the same can be said about those original particles where their history is not descriptively different and so on. But nevertheless we have two numerically different particles that are descriptively the same. I am not making the argument that such indiscernible identicals are at all possible, I am just saying resorting to ‘same history' doesn’t do the job. We will soon realise that we have to resort back to the notion of different/same space/time location' as some definitive point of difference, which brings me back to how we define 'same' and 'space/time'.
Now, to say that ‘if two objects occupied the same space wouldn’t they be just one’ doesn’t solve the problem for we haven’t demonstrated why that would be the case. Of course the assertion seems self-evident and intuitive but it nevertheless doesn’t represent at argument.
Now, I am not defending the position that such co-occupation is possible, I am merely saying that in my humble opinion the structure of the arguments need to be tightened.
Finally there is a difference between qualitative identity and numerical identity and the question is whether two objects that are qualitatively identical are necessarily numerically identical, or whether it is possible that they are in fact two numerically different objects. And how does the notorious 'space/time location' come into play.
This last point helps with confusions regarding 'everything is essentially made from the same thing' and so on. Any such comment needs to make clearly make the distinction between
qualitative vs numerical sameness and how they include or exclude one another .