How do we identify one particular particle that moves ?

[Spulbert]

Regarding a quantum leap, a particle goes from one place to another instantaneously - it is said - say an electron switching between levels.

If a particle were to switch from one place to another, how would you know it was one particle moveing in space, and not two particles alternately appearing and disappearing ?

I have never seen anything to say that one electron is distinguishable from another - they are not like dogs whereby you can say that it is definitely your dog moving from one place to another because you recgnise his coat.

Surely the existence of distinguishing features is one of the fundamentals of recognising an object, and if uniquely distinguishing features are missing then you cannot say that you recognise an object, and therefore cannot identify it, and single it out from all the others, to say that it moved ?

Isn't that fundamental unique identifier lacking in the subatomic world ?

 

[TheShrike]

It is! Particles that share all their properties (such as mass, charge etc) are indistinguishable. In particular, the statistical behaviour of bosons and fermions at low temperatures (e.g. Bose-Einstein condensation) is due precisely to their indistinguishable nature.

 

[Dale]

Hi Spulbert, welcome to PF!

What you say is essentially correct. There are no ID tags on electrons, so one is essentially the same as the other. However, I think that the "quantum leap" is a little misunderstood here. It isn't that an electron moves from one definite location to another definite location instantaneously, rather it is that the electron doesn't have a definite location at all until you measure it, and the possible locations are separated by a region where it definitely is not located.

 

[jtbell]

Regarding a quantum leap, a particle goes from one place to another instantaneously - it is said - say an electron switching between levels.

If you look carefully at the energy states of a hydrogen atom (for example), you find that although the energies are discrete and distinct, they don't correspond to discrete spatial "orbits," but rather, smeared-out probability distributions. The probability distributions for different energy levels overlap a lot, so an electron that "jumps" from one energy state to another doesn't have to "jump" in position also.

 

[Spulbert]

Thanks, good answers because I was wondering how it would play when looking at it less simplistically. The everyday language of electron shells, quantum leaps etc. naturally makes one think in a certain way - of particles as whizzing pellets.
But if one where to consider identical particles moving in discreet steps I would ask how we know it is the same particle we are watching - rather than several identical looking ones appearing and disappearing. Analogous to a monitor screen where the switching on and off identical pixels makes it look like the same object is moving.

 

[MikeGomez]

if uniquely distinguishing features are missing then you cannot say that you recognise an object, and therefore cannot identify it, and single it out from all the others, to say that it moved ?

What you can do is make an inference based on the physics of the object. If you catch a ball that I have thrown to you, do we really know whether or not the ball I threw is the same one you caught? From your previous statement it seems that you would argue that the ball has some distinguishing features which would allow us to recognize it, and therefore we could determine that it is indeed the same.

That is fair. However, what if we could not find our distinguishing features on the ball? Would we doubt whether or not the ball you caught was the same one I threw? Probably not, because we watched the flight of the ball, and we know from experience what a reasonable path for a ball in flight looks like.

So we really we don’t need to recognize the ball exactly, in order for us to be satisfied that the ball I threw is the same one you caught. We only need the ball that you caught to have a reasonably similar appearance to the ball that I threw. The important point here is the role that the laws of kinematics played in making the ball recognizable. The ball that you caught was found at the expected position and time as the ball that I threw.

The same idea applies to particles which can not be distinguished from each other. We first make a measurement and determine a particle or object to be at a given location at a given time with a given momentum, etc. We then use the kinematic equations to calculate a theoretical new position at a slightly later point in time. If we find a particle there similar to our original particle, it would be reasonable for us to treat that particle as the original one, and not fret over whether or not it might have gotten swapped with one of similar characteristics.

But if one where to consider identical particles moving in discreet steps I would ask how we know it is the same particle we are watching - rather than several identical looking ones appearing and disappearing.

Regarding the your concern about knowing whether particles taking “discreet steps” are the same, the short answer is that we don't know, however...

It doesn’t matter whether we think of the motion path of a particle as continuously smooth or in discreet steps. By that I mean that if we are concerned that a particle taking discreet steps (disappearing from one location and re-appearing in the next location) might not re-appear as the exact same particle, then we can also have the same concern with a particle with a continuous path. What’s preventing us from saying that a particle following a discreet trajectory might continuously be changing into another particle with identical features?

In the above example with the ball, did the ball take a continuous path or discreet steps? The ball is, after all, composed of subatomic particles, and if these particles are constantly disappearing and re-appearing with identical ones then it follows that the ball (as a whole) that was caught is, in some sense, not the exact same original ball as thrown.

 

[Spulbert]

What you can do is make an inference based on the physics of the object. If you catch a ball that I have thrown to you, do we really know whether or not the ball I threw is the same one you caught?
From your previous statement it seems that you would argue that the ball has some distinguishing features which would allow us to recognize it, and therefore we could determine that it is indeed the same.

I would, yes, a ball tends to gather distinct patterns of marks making it unique.

That is fair. However, what if we could not find our distinguishing features on the ball? Would we doubt whether or not the ball you caught was the same one I threw? Probably not, because we watched the flight of the ball, and we know from experience what a reasonable path for a ball in flight looks like.

That's right, we'd watch it all the way from one person to the other.

So we really we don’t need to recognize the ball exactly, in order for us to be satisfied that the ball I threw is the same one you caught. We only need the ball that you caught to have a reasonably similar appearance to the ball that I threw. The important point here is the role that the laws of kinematics played in making the ball recognizable. The ball that you caught was found at the expected position and time as the ball that I threw.

Hmm, I wouldn't go so far as to include laws in this case. Our everyday experience seems to be that if an object maintains the same unique pattern then it is the same object over time and space, that seems to be a fundamental which we need before we start to devise laws over the top of that experience.
ie, if galileo had dropped his ball from the Pisa tower and it looked profoundly different when it hit the ground he would have a challenge
And if it disappeared from his hand and an identical object instantaneously appeared on the ground, he would have an even bigger challenge!

Regarding the your concern about knowing whether particles taking “discreet steps” are the same, the short answer is that we don't know, however...

It would be easy to take the unknown to absurd lengths at this point - like asking how we know the particle is not a hologram particle created by an alien, or whether the entire universe didn't just dissappear and appear replaced by another identical one. We can paint anything into the gaps created by our lack of omniscience, but I wonder what is the basis for the painting we take for granted conventionally as being the way things are.

It doesn’t matter whether we think of the motion path of a particle as continuously smooth or in discreet steps. By that I mean that if we are concerned that a particle taking discreet steps (disappearing from one location and re-appearing in the next location) might not re-appear as the exact same particle, then we can also have the same concern with a particle with a continuous path. What’s preventing us from saying that a particle following a discreet trajectory might continuously be changing into another particle with identical features?

We can have that concern about a large object taking discreet steps, and how do we not know that a particle is changing into another all the time ?

Isn't the problem that we began thinking of motion based on our experience of the sensory world, but the same macro experiences don't carry over very well into a micro world which we cannot see directly and which is modeled by idealisations ?

When we talk about particles, we are really talking about our idea of particles aren't we ? Nobody actually sees an electron in the same way as we see the ball thrown in the park.

In the above example with the ball, did the ball take a continuous path or discreet steps? The ball is, after all, composed of subatomic particles, and if these particles are constantly disappearing and re-appearing with identical ones then it follows that the ball (as a whole) that was caught is, in some sense, not the exact same original ball as thrown.

Well, if you consider that the ball may oxidise a little, some water may evaporate from it's material etc., then you may indeed, strictly, have a different object, so there must be some change threshold that we accept as defining the ball as the same or a different object. We wouldn't normally say we have a different ball, though, we would just say that it is the same ball but changed a little.

And your point about appearing and disappearing particles, does that actually happen to any extent ?

 

[Khashishi]

You have to sum over amplitudes from all paths from state 1 to state 2 to get the total amplitude. You can't say which path the particle/system actually took, because the math says every path contributed. So, for an electron jumping from one state to another, you have to, in principle, consider situations where the electron was captured by the nucleus and "another" electron was emitted from the nucleus, or the electron annihilates with a positron which came out of nowhere, and a new electron and positron are produced. But, these paths contribute such a tiny amplitude that they probably can just be neglected.