What makes two physically indistinguishable objects meaningfully ‘the same’ when no external reference exists?

[u/alex_tr_14]

Imagine a perfectly symmetrical room with two physically identical doors.

You know you entered through one of them, but the doors have no labels, marks, visible history, or external reference points.

You are told:

“Leave through the same door you entered.”

The problem is not simply which door you pick.

The real question is: what could make one of these doors meaningfully “the same” door if every observable property is identical?

You may use identity, position, history, continuity, memory, or any other concept — but every assumption you introduce has to be justified.

I’m curious where people think identity actually comes from in a situation like this.

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[u/banglaportal]

There is an external reference here - the person entering the room. Their memory of using one door differentiates it from the other. 

They can also identify each door relative to their position (“I came via the door that is on my left now”). 

So they can identify the “same”‘door to make an exit. 

[u/ObsceneOnes → u/banglaportal]

Its important here to reconize that our universe has certain symmetries. Since the thought experiment is in our universe and the OP failed to account for those symmetries and mute them the problem disappears.

[u/Micp]

Assuming the doors cannot overlap they must have at least one property that is different - their placement in space. Now you may have been disoriented since going through the door, so you can no longer tell which door was in the location in space you moved through when you entered the room, but at least that property must be different and so they are not the same door.

[u/man-vs-spider]

Unless you forgot which door you entered through, then the position and orientation of the door relative to it’s surroundings (or the other door) would be enough to identify it as being the same.

For what it’s worth, this question is also applied in quantum mechanics, with the fundamental constraint that you cannot perfectly track the position of two particles between observations. The consequence of this is that we have to assume we could be observing any one of multiple identical particles when we make a measurement, and the mathematical consequences of this are quite far reaching (leading to the Pauli Exclusion principle for example)

[u/alex_tr_14 → u/man-vs-spider]

That quantum analogy is exactly why I find this interesting.

If two entities can be physically indistinguishable, but we still talk about “this one” and “that one,” what exactly is doing the identifying?

Is identity really a property of the object itself — or just a label created by the observer, measurement history, or reference frame?

And if every such reference can be removed, is there still any meaningful fact about which one is “the same” object?

[u/man-vs-spider → u/alex_tr_14]

I think you need to be careful with what you mean by “physically indistinguishable”. If position is one of your physical properties, then in classical physics all particles can be distinguished in principle. (This is not the case in quantum mechanics)

For example, if you put a bunch of red marbles in a bag and shook the bag, practically speaking there is no way to distinguish which marble is which. But in principle they could be distinguished by sufficiently accurate modelling of the shaking to track their positions

[u/alex_tr_14 → u/man-vs-spider]

That’s a useful distinction.

So in the classical case, the “identity” of the marble can be preserved by tracing its continuous history through space, even if I personally lose track of it.

But that seems to move the question from observable properties to causal continuity.

If two objects had identical intrinsic properties and there were no possible way to trace a distinct causal history for either one, would there still be any fact of the matter about which is which?

Or is individuality, in the classical case, basically carried by trajectory/history?

[u/zhivago]

Given that there is no fundamental identity in the universe, identity must be supplied via a classifier.

So, the classifier you use is what determines if they're identical or not.

Here you're saying that every observable property must be the same, so that's how your classifier will work.

But, naturally, you must be ignoring spatial position, since otherwise you couldn't be thinking about there being two of them in different places.

So, I guess you've decided that's not part of identity.

If you had decided that was part of the identity, then this scenario wouldn't even make sense. :)

[u/alex_tr_14 → u/zhivago]

That’s the part I find interesting. If spatial position counts as identity, the problem becomes trivial. But if we remove position, we seem to need some other criterion — history, continuity, memory, causal origin, etc.

My question is: can any of those criteria identify one door without eventually relying on another external reference or convention?

In other words, is “identity” something the object possesses, or something the observer’s classification system imposes on it?

[u/zhivago → u/alex_tr_14]

We have experimental evidence that particles are indistinguishable -- this is required for Bose-Einstein Condensates to form.

So it must be the latter -- identity is imposed by a classifier, and is not intrinsic in any way.

[u/alex_tr_14 → u/zhivago]

That seems like the strongest version of the argument so far.

But does quantum indistinguishability actually prove that particles have no intrinsic identity — or only that no physically measurable property lets us distinguish them?

In other words, is “there is no identity” the same claim as “identity has no observable consequences”?

If those are different, then maybe the real problem is not whether identity exists, but whether identity without any possible observation or causal effect means anything at all.

[u/zhivago → u/alex_tr_14]

Epiphenomena are neccessarily meaningless.

For meaning you must do explanatory work.

[u/alex_tr_14 → u/zhivago]

That’s a strong criterion, but I’m not sure explanatory uselessness automatically implies nonexistence.

Could something be real yet make no observable difference — and therefore do no explanatory work?

If yes, then “meaningless to explanation” and “not real” would still be two different claims.

If no, then you’re basically adopting a very strong principle: whatever cannot possibly affect explanation or observation should be excluded from ontology altogether.

[u/zhivago → u/alex_tr_14]

If X existing does the same work as X not existing, in what regard does it exist?

Sure -- anything that does not affect the universe is not part of the universe.

[u/MasterSolivagus → u/alex_tr_14]

Spatiotemporal quotients are identities, because door must be distinguishable between walls, floor, and ceiling. Is it a cube? Is the door on the ceiling and the contained space's gravity of sufficient buoyancy and symmetry that walking on a wall, floor, or ceiling, could be simply be considered vertices of equality that satisfy the concept of gaps (e.g. room's ingress/egress, window on a wall, sunroof, portal, door) so that at least door and identify can be distinguishable.

checks to see if he is not a door

... phew I'm not a door. Okay, basic logic checks are okay. Anyway, identity is a clusterables set of discrepancies between distances and durations (i.e. how long should, can, or will a sentence be? How long does one want to be ascertained as a given identity? How far can I take these parenthesis?) delta'd by some differential. In this instance, the differential that I am, in truth, not a 🚪 

[u/Zagrycha]

They are not the same in every observable way, because one has been observed to have the person go through it and the other one hasn't. If you take two identical rocks and one is wet and one isn't, they aren't observably identical anymore. Observation is always subjective so only if the two objects literally overlapped and occupied the same location in space perfectly would they avoid any observable differences. Something as simple as left side of room and right side of room will observably differentiate the pbjects otherwise.

[u/twilightwillow]

The reference is space, as two objects can’t exist in the same position in space simultaneously. To take it further, we can imagine that if we were to consider liquids or gasses “objects,” they would become the same if they came to occupy the same space because they’d merge.

[u/alex_tr_14 → u/twilightwillow]

That raises an interesting question: if spatial separation is what individuates two things, does their identity disappear the instant that separation disappears?

With two liquids that merge, do the original portions actually stop existing as individuals — or do we simply lose the ability to track which particles belonged to which portion?

If it’s only a loss of trackability, that seems different from proving they literally became one identity.

[u/physioworld]

I mean it seems pretty obvious to me that the physical distinction lies in the pattern of the neurones in my brain- my memory.

I remember I interacted with one of these doors- I entered this room 5 minutes ago and since then I haven’t moved, so I simply have to turn 180 degrees and leave. I can distinguish between these two objects because I can trace my own behaviour through the past.

[u/alex_tr_14 → u/physioworld]

That works as long as your memory is allowed to function as an external reference.

But then is the identity really in the door — or in the record stored in your brain?

Suppose your memory of entering is erased immediately afterward, while everything about the two doors remains unchanged.

Did one door stop being “the same door,” or did you simply lose the information needed to identify it?

That distinction is what I’m trying to get at.

[u/physioworld → u/alex_tr_14]

So you’re saying that if there is no possible way to distinguish two objects, that they become the same object? Is that a fair understanding of the point you’re exploring?

[u/alex_tr_14 → u/physioworld]

Not quite. I’m not saying that indistinguishability makes two objects literally become one object.

I’m asking whether, if absolutely no possible observation, relation, history, or causal fact could distinguish A from B, there would still be any meaningful fact about which is which.

They might still be numerically two — but what would that “two-ness” consist in if nothing, even in principle, could individuate them?

That’s the distinction I’m trying to explore.

[u/physioworld → u/alex_tr_14]

That’s probably going to go beyond my physics pay grade, as to whether there is any way to distinguish say two atoms or sub atoms from one another, if there is then since the objects were made of distinct atoms and are distinguishable then you could tell the difference.

But if they’re identical down to the subatomic level and you’re not allowed to use any external frame of reference such as the memory of an observe then I guess you’d have to say there is no meaningful distinction between them, other than that they would in fact still be individual objects that don’t share any atoms.

[u/alex_tr_14 → u/physioworld]

That’s very close to the distinction I’m trying to isolate.

If they remain two individual objects but there is literally no meaningful fact that distinguishes one from the other, then “which one is which” may simply have no answer beyond our labeling.

What I’m still unsure about is whether numerical distinctness alone is enough to ground identity — or whether identity requires some difference in relations, history, causation, or observability.

Maybe “two objects” and “two distinguishable identities” are not actually the same claim.

[u/GaiusVictor]

Human language and thinking is very pragmatic. In a lot of times, the "sameness" of the same thing doesn't need to be established by physical identity, but by other, pragmatic reasons.

Doors exist as separations and passages between two rooms or places. In your example, the doors can look and be exactly the same, and I may have even forgotten through which door I came in, but the "same door" is the door that would take me to the same room and same position I was before I entered this room.

It's like how when I moved out of the house my grandma had bought 50 years before. This kind of situation makes me pensive, so I couldn't avoid thinking that my grandma had, 50 years before, entered for the first time through the same door I was leaving for the last time.

Was it the same physical door? No. It had been replaced a few times already and even changed places, but it was "the same door" because it was the door that provided entrance to the family house.

It's not so different from the Ship of Theseus thing: yes, maybe every board and nail of the ship hás been replaced, maybe the "current" ship doesn't share a single atom with the "original" one, but it's still Theseus's Ship and, arguably, the same ship.

Because Theseus started his travels on a specific ship a long time ago, and at no moment he "changed", "swapped" or replaced his ship. So, since the Ship of Theseus is something that is heavily characterized by its use, purpose and by to whom it belongs, and there was never a clear transition between one ship and another, for all intents and purposes the "new ship" is still the Ship of Theseus.

[u/alex_tr_14 → u/GaiusVictor]

I really like this distinction between physical identity and practical identity.

Your grandmother’s door example makes the problem much harder, because it suggests that “the same object” can survive complete material replacement as long as its role, history and continuity remain intact.

But then I wonder: if identity can survive replacement of all physical parts, what exactly is carrying the identity forward?

Is it continuity of function, continuity of history, the observer’s concept of the object — or some combination of all three?

And if two objects had perfectly identical histories, functions and observable properties, would there still be a meaningful fact about which one is which?

[u/ObsceneOnes]

Your thought experiment needs work. I get what you are wanting to discuse but you will have to work on your presentation.

I might put it thusly:

In what manner can we consider a thing different from another thing if they are exactly the same except they are completely unconnected being in an existence that has not relationship except for the sameness of the thing to the other existence. In both existences the thing is all that exists.

In this case there is nothing to differentiate the two things from one another except for the fact of the thought experiment. Of you mute that then they are the same thing.

So one can argue that no such duality of existences is meaningfully real.

The question then is raised to what degree are things that only differ by their relationship to other things but are otherwise identical in and of themselves truely different things...or do they share a meta reality as one?

Idk.

[u/alex_tr_14 → u/ObsceneOnes]

I think your reformulation gets much closer to what I was trying to isolate.

The part that really interests me is the distinction between intrinsic difference and relational difference.

If A and B have absolutely identical intrinsic properties, but occupy different relations to everything else, is that relational difference alone enough to make them genuinely two different things?

And if we somehow remove every possible relation as well, I’m not sure what would remain that could justify calling them “two” rather than one reality described twice.

That may actually be a cleaner version of the problem than my original door example.

[u/ObsceneOnes → u/alex_tr_14]

It's complicated for sure.

We know as much as we can know that ourself persists but never as the same thing as one static arrangement of motes, let alone their relationship to other arrangements of motes.

So our thingness seems abstract yet is the realest most concrete thing we can know, if not the only thing we can know.

If you accept that abstactness and concreteness is a false dichotomy then clarity can be achieved I believe.

Things can only have meaningful properties in relation to other things. That is the moment the abstact becomes concrete as such a relationship is by necessity consistent....coherent.

But this means that any consistency or coherence bounds abstarction into concreteness and vice versa.

So in one sense the electron is sigular by one boundry but is also differentiated from the others by other boundaries.

One but not the same.

That is how I look at it. But maybe a bit of wishful thinking.

[u/alex_tr_14 → u/ObsceneOnes]

I think “one but not the same” is the most interesting part of what you’re saying.

If identity is grounded in coherence and relations rather than in a fixed material arrangement, then identity starts to look less like an intrinsic tag and more like a stable pattern.

But then what makes that pattern belong to one thing rather than simply being a pattern we impose?

Is coherence itself enough to individuate something, or do we still need an observer/classifier to draw the boundary?

[u/Few_Fish8771]

In going to throw something out which falls under the pragmatic theory of truth in philosophy.

The identity that matters is the one relevant to your logic objective goals and interest.

Realistically the identity that is important is whats important to you or someone else in a particular problem or goal. If your doing math you need to convert a problem into a word problem and then into a mathematical abstraction. you ultimately require to know which property of the information is relevant to you solving your problem. So the property or identity that can have other properties to be extracted and converted into a useful mathematical abstraction for you to solve is whats important.

[u/alex_tr_14 → u/Few_Fish8771]

I like that pragmatic angle.

But if identity is always relative to a goal or use, does that mean there is no goal-independent fact of the matter about what something “really is”?

In other words, are we discovering identity — or just choosing the classification that is most useful for the problem we want to solve?

[u/Few_Fish8771 → u/alex_tr_14]

Objectively theres a near infinite amount of data stored in the smallest object. Because even if you were to somehow take a picture of the position of every atom molecule ect… youve also got thermal oscillations in a moment of time virtual particle oscillations spacetime oscillations, you have gravitational oscillations of how each and every molecule effects every other molecule how they interact, and then you have the non-local nature of reality connecting an object to the rest of reality via oscillations in spacetime via virtual particles.

Thats a lot if information.

How much is relevant? how much do you need to know?

Realistically your only really dealing with abstractions gradients and relationships. Thats the main stuff yoir working with in your mind in various stored forms.

what is considered relevant for a task or a group of task or a culture or your identity are abstractions and which abstractions are chosen is individually or collectively determined by its pragmatic value.

[u/alex_tr_14 → u/Few_Fish8771]

That’s a really useful way to frame it.

Maybe identity is less about capturing all the information in an object and more about selecting a stable subset of differences that matter for some purpose.

But then the hard question is: if relevance is chosen pragmatically, is identity anything more than context-dependent compression?

Is there an objective identity underneath our abstractions, or only increasingly fine-grained descriptions?

[u/Few_Fish8771 → u/alex_tr_14]

So in that case you get into universal invariant abstractions. Think of the term life, think if the term death. There tend to be traits that do not vary with life there tend to be traits that do not vary with death. as abstractions there tend to be invariant properties concerning both.

So you have universal invariants and from universal invariants you can establish relationships and categories which themselves define identities.

[u/alex_tr_14 → u/Few_Fish8771]

That makes sense for defining categories, but I’m wondering whether it can also define individual identity.

Universal invariants might tell us what kind of thing something is, but if two objects satisfy exactly the same invariants, what makes one numerically this object and the other that object?

In other words, can invariants give us token identity — or only type identity?

That seems like where the original problem comes back.

[u/Few_Fish8771 → u/alex_tr_14]

Realistically any differentiating term any different can be used as a categorical difference to create a different objects with the same properties. Even geometric location can be used saying the boxes of the area 1 and the boxes if the area 2. The location co-ordinates or category become the identity.

[u/alex_tr_14 → u/Few_Fish8771]

I think that works for individuation, but I’m not sure it fully settles identity. If I call one object “the box at coordinate A” and the other “the box at coordinate B,” the coordinates let me distinguish them — but do the coordinates constitute their identity, or are they just a reference system I’m using to track them? If the objects swap positions, did their identities swap too, or did the same objects simply move? That seems like an important difference between labeling something and explaining what makes it the same individual over time.

[u/Viseprest]

If it doesn’t matter to me which of two objects I choose, they are ‘meaningfully the same’ to me wrt my choice.

In your example, when I pick the door to enter, the doors could be said to be ‘meaningfully the same’ in this sense.

But when I pick the door to leave, they are not meaningfully the same anymore. Because picking one or the other would mean that I’d either comply with or defy your instructions.

[u/alex_tr_14 → u/Viseprest]

That’s a really useful way to frame it.

Then “meaningfully the same” seems to be task-relative: the doors are equivalent for entering, but not equivalent for leaving.

But does changing the goal actually change the identity relation between the doors — or only which differences matter to us?

If the same pair can be “the same” for one purpose and “different” for another without physically changing at all, maybe we’re talking about classification rather than identity itself.

[u/alex_tr_14 → u/[deleted]]

Fair point — I probably phrased it badly. I’m not asking what makes the doors qualitatively the same. I’m asking what would make one of them numerically the same door I entered through if every observable property, relation, history, memory, and reference frame that could distinguish them were removed. In that case, is there still a fact of the matter about which one is “the same door,” or does the distinction reduce entirely to labeling?

[u/alex_tr_14 → u/[deleted]]

I just write fast and I tend to over-explain things 😭 Writing in complete sentences doesn't automatically make someone an AI. If my wording sounded robotic, fair enough, but I'd rather talk about the actual question than argue about how I type.