Exploring the Differences Between Two Identical Hydrogen Atoms

[Wondermine]

Elementary my dear Watson. A simple question that is perhaps not so simple. But maybe it is elementary or simple.
It is: There are two Hydrogen atoms side by side. It is said they are identical in that they are made of exactly the "same" components.
The question is what makes them different?
There are two of them so they must differ. What makes them different if they are termed "the same".

 

[mjc123]

They are not "the same" atom. But they are indistinguishable - if they swapped places while your back was turned, you wouldn't be able to tell.

 

[CWatters]

Position
Orientation (if a molecule)
Temperature?

 

[davenn]

There are two of them so they must differ. What makes them different if they are termed "the same".

why do you think they must differ ? ... if they are different, then one of them cannot be a hydrogen atom

 

[LURCH]

why do you think they must differ ? ... if they are different, then one of them cannot be a hydrogen atom

I think he’s referring to the fact that there are two of them. Something must make them two hydrogen atoms, and not one.

 

[ZapperZ]

Elementary my dear Watson. A simple question that is perhaps not so simple. But maybe it is elementary or simple.
It is: There are two Hydrogen atoms side by side. It is said they are identical in that they are made of exactly the "same" components.
The question is what makes them different?
There are two of them so they must differ. What makes them different if they are termed "the same".

Is this a physics question or a statistics question?

Zz.

 

[andrew s 1905]

Elementary.

How many "e" are there in Elementary. I would say 3, two are identical in form but they are not the same one as there are two of them.

Regards Andrew

 

[davenn]

I think he’s referring to the fact that there are two of them. Something must make them two hydrogen atoms, and not one.

of course he does

my answer still stands

 

[Nugatory]

It is said they are identical in that they are made of exactly the "same" components.

When we're being careful with words (more careful than in informal conversation), we will say "indistinguishable" instead of "identical". When we want to rigorously describe the system, we don't use English or other natural language at all, we start with a two-particle wave function.

 

[DaveC426913]

Position
Orientation (if a molecule)
Temperature?

This seems like the simplest answer.
Look at the OP's question:

There are two of them so they must differ.

Just because there are two doesn't mean their differences must be internal - the thing that is different is their circumstances wrt to their environment - such as CWatters' position, orientation and motion.
(Note, BTW that all three of those circumstances require an external reference frame to be meaningful.)

 

[PeroK]

This seems like the simplest answer.
Look at the OP's question:

Just because there are two doesn't mean their differences must be internal - the thing that is different is their circumstances wrt to their environment - such as CWatters' position, orientation and motion.
(Note, BTW that all three of those circumstances require an external reference frame to be meaningful.)

These are transient dynamic properties of the atoms and not permanent identifying features. If you have two electrons, one spin up and one spin down, that does not mean you can distinguish them. All you can say is that one is up and one is down. The statistics follow the rule that there are not two possibilities here. This is unlike, say, identical coins or snooker balls, where the statistics are different and you have two different possibilities: coin A heads, coin B tails; and coin A tails, coin B heads.

That's a fundamental distinction that nature draws between indistinguishable particles and objects that can be distinguished - even if the experimenter cannot identify one coin from another.

 

[DaveC426913]

These are transient dynamic properties of the atoms and not permanent identifying features. If you have two electrons, one spin up and one spin down, that does n ot mean you can distinguish them.

... Agree?

I think you're concurring with me. What distinguishes the two otherwise indistinguishable atoms in the OP is simply their relationship to the frame of reference, not some internal property.

 

[PeroK]

... Agree?

I think you're concurring with me. What distinguishes the two otherwise indistinguishable atoms in the OP is simply their relationship to the frame of reference, not some internal property.

No. They are still indistinguishable. And the allowable wavefunctions and statistics will reflect that.

 

[PeroK]

... Agree?

I think you're concurring with me. What distinguishes the two otherwise indistinguishable atoms in the OP is simply their relationship to the frame of reference, not some internal property.

PS This might interest you:

https://en.wikipedia.org/wiki/One-electron_universe

 

[DaveC426913]

No. They are still indistinguishable.

Sorry, I think you are reading more into it than I intend.

The OP's question - the part that I'm concentrating on - is that "there are two of them so they must be different".

I read that as the OP saying that, if they were utterly indistinguishable, then we would somehow only see a single atom in front of us. As if two indistinguishable things cannot co-exist by-side-side, for some reason.

My response is simply that the only way they are distinguishable is that one is at these spacetime coordinates, and one is at those spacetime coordinates. It's trivially true.
But more: no internal property makes them unique.

Does that clear it up?

PS This might interest you:
https://en.wikipedia.org/wiki/One-electron_universe

Indeed. It did interest me - many years ago, when I first encountered it.

 

[Wondermine]

I think he’s referring to the fact that there are two of them. Something must make them two hydrogen atoms, and not one.

Yes,that is what I thought. If they were the same then there would only be one. perhaps location makes them different. If this is true then location is an intrinsic property of "stuff" is it not? In reference to Bohm then
could "they" be the same exactly ,in essence one thing, emergent in 2 locations at slightly different times(out of phase in time so to speak)? So it is also a question of the correctness of emergent ideas. What is the general view of this?

 

[A. Neumaier]

Position
Orientation (if a molecule)
Temperature?

Only position and angular momentum. A single hydrogen atom (as in the OP) has neither orientation nor temperature.

My response is simply that the only way they are distinguishable is that one is at these spacetime coordinates, and one is at those spacetime coordinates. It's trivially true.
But more: no internal property makes them unique.

If you regard angular momentum as an internal property, your last statement is incorrect.

Position and angular momentum distinguish the otherwise indistinguishable particles. The term ''indistinguishable'' refers to the kind of particle, while position and spin refer to its contextual properties (when measured). One distinguishes them by talking about ''the hydrogen atom here'' vs. ''the hydrogen atom there'', or ''the hydrogen atom with angular momentum in this direction'' vs. ''the hydrogen atom with angular momentum in that direction''.

But it is possible for several indistinguishable atoms to be in exactly the same state. This happens in a Bose–Einstein_condensate and has been demonstrated for Rubidium atoms. These form a Bose–Einstein_condensate at low enough temperature (170 nK), and lead to the 2001 Nobel prize in Physics.

 

[DaveC426913]

... location is an intrinsic property of "stuff" is it not?...

No, it is an extrinsic property.

 

[PeterDonis]

it is possible for several indistinguishable atoms to be in exactly the same state. This happens in a Bose–Einstein_condensate

Wouldn't it be more correct to describe a Bose-Einstein condensate as a system containing multiple bosons that is, as a system, in a state in which the individual bosons do not have definite states (because they are all entangled)?

 

[Wondermine]

So from what was said is it then possible to construe that there is only one hydrogen atom and that all of the numerous hydrogen atoms are merely possible states of this one atom in an infinite iteration of possible external influences.(different time,location,spin ,magnetic moment etc.

These are transient dynamic properties of the atoms and not permanent identifying features. If you have two electrons, one spin up and one spin down, that does not mean you can distinguish them. All you can say is that one is up and one is down. The statistics follow the rule that there are not two possibilities here. This is unlike, say, identical coins or snooker balls, where the statistics are different and you have two different possibilities: coin A heads, coin B tails; and coin A tails, coin B heads.

That's a fundamental distinction that nature draws between indistinguishable particles and objects that can be distinguished - even if the experimenter cannot identify one coin from another.

Let me ask this question. Do all of the electrons of "all" of the Hydrogen atoms have the same spin? Can the spin of one electron on one Hydrogen atom be opposite to the spin of an electron in another Hydrogen atom?
Secondly,can extrinsic influences change the spin of the electron,or is the spin of an electron of an Hydrogen atom locked as an unchangeable property(intrinsic) to that H atom?

 

[PeroK]

So from what was said is it then possible to construe that there is only one hydrogen atom and that all of the numerous hydrogen atoms are merely possible states of this one atom in an infinite iteration of possible external influences.(different time,location,spin ,magnetic moment etc. Let me ask this question. Do all of the electrons of "all" of the Hydrogen atoms have the same spin? Can the spin of one electron on one Hydrogen atom be opposite to the spin of an electron in another Hydrogen atom?
Secondly,can extrinsic influences change the spin of the electron,or is the spin of an electron of an Hydrogen atom locked as an unchangeable property(intrinsic) to that H atom?

First, I think you are getting philiosphy, not physics. There is one model for the hydrogen atom, but to say there is only one hydrogen atom is not physically meaningful. At the root of all this, you are simply struggling with the concept that at the smallest possible scale there is a set of elementary particles. There are a number of different types of elementary particle with some fixed properties (e.g. mass and charge) and some dynamic variables (position, momentum, spin), which are described by its quantum state. But, because these are elementary particles (or well-defined combinations of several elementary particles), they can only be put together in one way. That means that you cannot fundamentally distinguish one from another.

You could do with some basic understanding of QM. Spin is a dynamical property. A hydrogen atom will have a spin, which is roughly the sum of the spin of its constituent proton and electron. And, you could do with some understanding of the nature of two-particle systems, such as the Pauli exclusion principle.

 

[Wondermine]

First, I think you are getting philiosphy, not physics. There is one model for the hydrogen atom, but to say there is only one hydrogen atom is not physically meaningful. At the root of all this, you are simply struggling with the concept that at the smallest possible scale there is a set of elementary particles. There are a number of different types of elementary particle with some fixed properties (e.g. mass and charge) and some dynamic variables (position, momentum, spin), which are described by its quantum state. But, because these are elementary particles (or well-defined combinations of several elementary particles), they can only be put together in one way. That means that you cannot fundamentally distinguish one from another.

You could do with some basic understanding of QM. Spin is a dynamical property. A hydrogen atom will have a spin, which is roughly the sum of the spin of its constituent proton and electron. And, you could do with some understanding of the nature of two-particle systems, such as the Pauli exclusion principle.

I am not sure why you bring in the Pauli exclusion principle to my question since there is only one electron "in" the H atom. I am not sure whether there are "non" dynamical properties to either the quarks or the electron.
Although the questions can be interpreted as a philosophical matter they can be concerned with whether the atom is an emergent property of a universal as yet unmeasured filed of energy or is it a distinct entity in of itself.
If the former is true then the Bohm description of the double slit results would have some validity.
The questions are finding what others think about whether the H atoms are all identical with different locations or not all identical.
You suggest all quarks and all electrons are identical.
Would this not then support the reasoning that they are emergent properties of 1 field and that electrons are properties of 1 other field, both fields being intrinsic to all space but at an order of magnitude so as to be un measurable.
The Plank distance is derived from the emergent property,not from the intrinsic un changeable foundation finer field.
I will refrain from further questions on this.Thanks for your insight and suggestion. There is always more to learn and new angles to look at previous learned things. Interest is an emergent property of these states.

 

[PeroK]

I am not sure why you bring in the Pauli exclusion principle to my question since there is only one electron "in" the H atom. I am not sure whether there are "non" dynamical properties to either the quarks or the electron.
Although the questions can be interpreted as a philosophical matter they can be concerned with whether the atom is an emergent property of a universal as yet unmeasured filed of energy or is it a distinct entity in of itself.
If the former is true then the Bohm description of the double slit results would have some validity.
The questions are finding what others think about whether the H atoms are all identical with different locations or not all identical.
You suggest all quarks and all electrons are identical.
Would this not then support the reasoning that they are emergent properties of 1 field and that electrons are properties of 1 other field, both fields being intrinsic to all space but at an order of magnitude so as to be un measurable.
The Plank distance is derived from the emergent property,not from the intrinsic un changeable foundation finer field.
I will refrain from further questions on this.Thanks for your insight and suggestion. There is always more to learn and new angles to look at previous learned things. Interest is an emergent property of these states.

I guess we are coming at this from different directions. I know QM, but I don't know what an "emergent property" is. And, you, I presume, know what an emergent property is but don't know any QM.

 

[A. Neumaier]

So from what was said is it then possible to construe that there is only one hydrogen atom and that all of the numerous hydrogen atoms are merely possible states of this one atom

No. This is a severe misunderstanding. one can count the number of hydrogen atoms in a system, and this number can be any nonnegative integer. Having two indistinguishable atoms (whether in the same state or in different states) still means having two and not only one!

 

[PeterDonis]

Would this not then support the reasoning that they are emergent properties of 1 field and that electrons are properties of 1 other field

Have you looked at the Standard Model of particle physics? You are describing what it says: there is a field for each kind of fundamental particle (for example, electron, quark), and individual particles (electrons or quarks) are particular states of the corresponding field at particular points in spacetime. (The word "emergent" is superfluous here.)

The Plank distance is derived from the emergent property,not from the intrinsic un changeable foundation finer field.

I don't know what you mean by this, but it doesn't look like anything in the Standard Model. The Planck length has no special status in the SM. It does in various theories of quantum gravity, but all of those theories are speculative at this point since we have no way of testing any of them by experiment.

 

[PeterDonis]

This thread has run its course and is now closed.