Consider an atom of hydrogen at a time t, and the "same" atom of hydrogen at a time t + 1 second. Are those atoms really the same, or are they distinct? I believe they are distinct, because I think two objects can only be the same only if they are the in the same location at space-time. So, my question is, is one object at different times actually different objects? And have philosophers talked about this issue?
OK, let's take your example of a hydrogen atom. Does it maintain its "identity" over time?
Since it consists of one electron and one proton, the question becomes does that electron and that proton maintain its identity over time?
The answer to this question hinges on whether or not we can distinguish between two different protons and between two different electrons. Are they distinguishable? If so, then as time goes by we would have a basis for determining whether or not yesterday's electron is the same as today's electron, and the same for protons.
There is no aspect of either particle which would allow us to answer that question. All protons and all electrons are identical and carry no "identity flag" which would let us label one of them uniquely and thereby determine if its identity had changed within an atom in some way.
This means that if a hydrogen atom "lost" its electron which was then subsequently replaced by another different electron, we would have no way of knowing if that had happened.
This really hinges upon what we mean by identity and also how something maintains its identity over time. Its an ontological question.
The classical philosophical question on this is the Ship of Theseus. It runs roughly as follows: if we replace all the parts of the ship, is it still the same ship?
Now location is not generally seen as an intrinsic property of a thing. Location is what allows for movement and hence change. And so the question is can something change and still maintain its identity?
Well, there are two kinds of change. The first is intrinsic, like a water on a lake rippling. The other is external, like the motion of a train. Now, I've already discounted external properties as being reflective of identity. This leaves intrinsic properties and intrinsic change.
These can be divided into two kinds. Properties which though intrinsic, aren't essential to the identity of a thing and properties that are essential. For example, the shape of a lump of wax isn't essential to it whilst being soft and malleable is.
Now a hydrogen atom atom is constantly in flux. There is an electron cloud constantly in motion and a nucleus with three quarks in it and that is also constantly changing. Yet despite all this change in space and time, I would say that it is the same hydrogen atom. Its merely its parts that are in motion. Now just because a hydrogen atom has parts does not mean the hydrogen atom doesn't exist. A coherent assemblage is as just as much a thing as the parts it is made of. Its just a different thing from them.
In some sense, by denying identity over space and time, you are denying the possibility of change.
I mean the obvious counter example would be yourself. Like what if it's not a hydrogen atom but yourself and yourself in 1s. Would you argue that a tape recording of yourself shows "you" or "a different person"?
And probably the vast majority of people would argue it's you. Leading to concepts of the ship of theseus, asking how much change can happen before the identity is changed. Or sorities paradox as to when does a congregation of grains of sand becomes a heap or vice versa.
But if you go to the hydrogen atom, you might still have fluctuations in terms of different spin and energy states, that make it different and yet the same. Also you might have the very real problem that you can't measure the difference between hydrogen atoms, so for all realistic intents and purposes they actually are the same as there is no why to tell the difference between them. But if you argue that location is a property of the object and thus it becomes a different object "atom at xy" becomes "atom at xy'" you still run into a different problem namely that location is not absolute but subjective and/or relative, so you might not even be lucky to be able to use that as a property of the object itself.
What we know from current physics, is that both time and space - spacetime - is emergent phenomenon. Meaning, universe exists in some invariant form (wave function), and it only appears to some parts of that function (us) that the rest of the same function is "changing in time". So, object identity is useful tool (handle) we use in our lives to talk about what is going on.
What do you mean by object? If you include consciousness, then one consciousness through time is the same consciousness and does not change.
As for other objects; they have discontinuities throughout time (erosion, etc). Therefore, the answer is no.
Edit: BTW, from the point of view of special relativity, I believe the answer is no, because:
- The future and the past do not exist at the same time
- Time is a fourth dimension, and all objects travel in a straight line in the 4-dimensional hyperspace composed of the three spatial dimensions x, y, z and time t. Considering that the object is said to travel through time, I don't believe special relativity takes one object at different points in time to be multiple different objects.
Is one object at different times actually different objects?
From the logical point of view, the wording of the question provides the answer to it: Is one object ... ?
Logically, one object is one object, and there is nothing else to it. One object cannot be different objects. Time has nothing to do with the affair.
Rephrase if you want...
Can one object at time t and another object at time t + Δt be the same object?
No, simply because the second object is assumed from the start to be another object.
Can one object at time t and the same object at time t + Δt be the same object?
Yes, because, trivially, you start by talking of the same object.
Humans, all humans, obviously choose to talk of the same object as possibly existing at t and t + Δt. The philosopher will invariably conceive of his or her toothbrush in the evening as the same object as his toothbrush in the morning.
Each human see their own father as the same object throughout his life.
Someone who is the rightful owner of one 1 million dollars property in the morning will not accept that he is no longer the rightful owner of it in the evening simply because someone else points out that it is no longer the morning.
The same can be said about our own body.
No murderer will ever obtain a non-guilty verdict by arguing that the gun exhibited by the prosecution cannot possibly be the gun that was used to murder the victim.
Humans don't really have a choice. It is our brain that decides what is an object. If we had to think to be able to decide that our toothbrush in the evening is the same as our toothbrush in the morning, we would not stay alive very long. Philosophers are paid while they think deep thoughts, but most humans are not.
It is indeed a very complex process for a cognitive system to identify objects. Our brain does it, and it is not asking us our opinion.
Think also about the seriously costly and cumbersome process necessary to decide whether people are who they say they are.
Of course, this would also depend on what we think objects are but here again we don't really have a choice. The word "object" came to mean what it means today through linguistic usage, not logical reasoning. We inherited this notion from the long history of the notion of object.
I think two objects can only be the same only if they are the in the same location at space-time.
We can always redact definitions, but on penalty of ending up speaking a private language. This may work for obscure words few people ever use but the word "object" is much too common to be tinkered with.
Finally, there is no difficulty in the idea that an object at t is not the same thing as the same object at t + Δt. This is unproblematic, trivial and of no practical consequence.