Is scientific knowledge ultimately limited

[himanshu2004@]

Are two electrons identical in every way? I think that's what we know so far, but is there any research that proves/doubts this or any reason to expect why it should or should not be the case?
I ask because no two things in (the macroscopic) world are absolutely identical, and so I wonder if this would also ultimately be true of the microscopic world.

Also, I understand that assuming electrons/elementary particles to be point particles might be a helpful model or perhaps is all we can do at this point since we don't know their substructure or their size. But isn't the inherent ability to examine reality at successively tinier levels ultimately a problem for science to understand the nature of reality at the most fundamental level?

 

[ZapperZ]

Are two electrons identical in every way? I think that's what we know so far, but is there any research that proves/doubts this or any reason to expect why it should or should not be the case?
I ask because no two things in (the macroscopic) world are absolutely identical, and so I wonder if this would also ultimately be true of the microscopic world.

You might want to look at the indistinguishiblity statistics in quantum mechanics. Two identical objects in classical statistics follow the Maxwell-Boltzmann distribution, but you don't see them obeying the Fermi-Dirac of Bose-Einstein statistics the way indistinguishable quantum particles (such as electrons) do.

So what you are claiming does not follow empirical observations.

Also, I understand that assuming electrons/elementary particles to be point particles might be a helpful model or perhaps is all we can do at this point since we don't know their substructure or their size. But isn't the inherent ability to examine reality at successively tinier levels ultimately a problem for science to understand the nature of reality at the most fundamental level?

The reason why we need higher and higher energy collision is that the higher energy scale allows us to examine physics at shorter length scales. This has nothing to do with whether elementary particles are point particles or not. They are right now based on what we know best. But in physics, none of these things ever stopped us from looking further, deeper, and closer. That's why we continue to explore and expand the boundary of our knowledge.

Zz.

 

[himanshu2004@]

Thanks I will look that up. I wasn't claiming any thing; I just had a question :)

With respect to high energy collisions, I was wondering if their is a limit particles smaller than which we won't be able to observe? I mean would it not be limited in some way whatever thing we use to "observe". Like we can only observe things up to a certain size with light microscopes, and electron microscopes help us observe even smaller things, but how can we go arbitrarily far this way? Again, no claim, just a question :)

 

[Jadaav]

I would say that it has to stop at a certain point, which would make sense. Can you imagine yourself made up of something infinitely small ? I guess, not.

What I know of is that, there can't be something infinitely small in a definite place, correct me if I'm wrong here please.

 

[himanshu2004@]

I am not saying that the smallest "fundamental particle(s)" would be infinitely small, for that is a contradiction in terms. What I was wondering if there is a limit beyond which science won't be able to probe in terms of finding successively smaller particles, because we would have no means of observing those.
I am not saying I think it is so; I am asking if and how we are sure that this is not the case.

 

[Bloodthunder]

Physics has a problem with observing subatomic particles. Uncertainty principle and all that.

 

[Drakkith]

Is it possible that some particles are simply to small to detect? Sure! But unless we have some reason to believe that they exist there isn't any real reason to talk about them seriously. If we found reactions or collisions that resulted in missing mass that we couldn't explain then that would open up the discussion though.

 

[vkroom]

With respect to high energy collisions, I was wondering if their is a limit particles smaller than which we won't be able to observe?

Yes! Theoretically one cannot observe beyond the Planck`s length because the uncertainty principle will imply energies large enough to form black holes. Consequently one may not obtain information beyond such black holes. In this sense with our current understanding of Nature one may assume Planck length to be the highest energy that may be accessed.


About your first question : By the definition of the term `fundamental`, a fundamental particle is not made up of anything else, therefore it is unique in its features and hence all fundamental particles of the same type are identical.

 

[Curl]

You might want to look at the indistinguishiblity statistics in quantum mechanics. Two identical objects in classical statistics follow the Maxwell-Boltzmann distribution, but you don't see them obeying the Fermi-Dirac of Bose-Einstein statistics the way indistinguishable quantum particles (such as electrons) do.

I don't see how the statistics have anything to do with indistinguishiblity. All three treat indistinguishable particles, the only difference is that in Boltzmann statistics there is no chance of 2+ particles occupying the same quantum state.

Indistinguishiblity at the quantum level is due to the wave function, since it is independent of the actual particle representing it. As long as it has the same mass and charge, there is no way it can be "different". And since things are quantized at that low of a level, you can't say "this electron has 1% more charge than this one" or anything like that.

 

[himanshu2004@]

Yes! Theoretically one cannot observe beyond the Planck`s length because the uncertainty principle will imply energies large enough to form black holes.

Thanks for pointing out this theoretical limit. Also, found that even if we assume Planck length to be a theoretical limit, it seems we haven't been able to observe nature many many orders of magnitude anywhere close to that. From Wikipedia:
The Planck length is about 10⁻²⁰ of the diameter of a proton, and thus is an extremely small length. It is much smaller than the smallest length values ever measured or probed, which are about 10⁻⁵ of a proton diameter.
So we the tiniest levels of reality we have examined are a colossal 10¹⁵ times bigger than Plank size!

About your first question : By the definition of the term `fundamental`, a fundamental particle is not made up of anything else, therefore it is unique in its features and hence all fundamental particles of the same type are identical.

Yes, I have understood now that these particles are indeed exactly identical. But so are atoms of Hydrogen for example. So it doesn't mean that we can be sure if they are indeed fundamental (which of course you never claimed). So not only are we not sure whether these are the fundamental particles, from my limited understanding, it seems rather unlikely that we would ever even be able to examine reality at really really close quarters, limited both theoretically and practically. Of course in the generations to come science will continue to make progress but I think pushing the boundaries of how closely we can understand reality will get harder and harder with each order of magnitude, and we might be able to go only so far even if we ignore the theoretical limit beyond which things seemingly become spooky!