Fermions vs Bosons: Low Temp Effects

[nouveau_riche]

why is that at relatively low temperature bosons can occupy the same state while the fermions cannot?
and how does we macroscopically see the effects of bosons (with explanations)?

a theoretical answer is preferable

 

[Simon Bridge]

Um - because Fermion obey the Pauli exclusion principle?
That's pretty much part of the definition of "fermion" ... which leaves: how come spin 0.5 particles also hot their quantum states?

"because that is how the Universe works" is the bottom line.
Physics does not answer "why" questions very well.

I remember there is something about the symmetry involved in spin half particles that means that they cannot share states. But it is just modelling the physics we find in the real world. You realize that Physics is an empirical science right?

 

[nouveau_riche]

"because that is how the Universe works" is the bottom line.
Physics does not answer "why" questions very well.

You realize that Physics is an empirical science right?

let me phrase it in the way physics would like

In the early stages of universe, just after the big bang at the moment when particles start to get their properties and dimensions how it is that a particle will become a Fermion or a boson?
or is there any possibility that a fermion can become a boson?

 

[Dale]

or is there any possibility that a fermion can become a boson?

Certainly. You can have a positron and an electron which decay into a pair of photons, and you can also have the reverse.

 

[jarod765]

So your question is about the beginning of the universe then?

Since we do not know the physics or the initial conditions of the universe at the earliest scales then we cannot certain how particles "gained" their statistical properties.

If we try and approximate using field theory however we can get an intuition about it. Here is my intuition about it:

1) In field theory particles live in representations of a symmetry group.

2) Depending on which representation it lives in then it will have either integer or non-integer spin.

3) For various technical reasons a field with integral (half-integral) spin will obey commutation (anti-commutation) relations.

4) the commutation relations make explicit which statistics a particle will obey (note: statistics implies the exclusion principle).

As for how many and what type of fermions and bosons were created at the early universe that has to do with the mechanisms of inflation and reheating processes.

 

[nouveau_riche]

So your question is about the beginning of the universe then?

Since we do not know the physics or the initial conditions of the universe at the earliest scales then we cannot certain how particles "gained" their statistical properties.

If we try and approximate using field theory however we can get an intuition about it. Here is my intuition about it:

1) In field theory particles live in representations of a symmetry group.

2) Depending on which representation it lives in then it will have either integer or non-integer spin.

3) For various technical reasons a field with integral (half-integral) spin will obey commutation (anti-commutation) relations.

4) the commutation relations make explicit which statistics a particle will obey (note: statistics implies the exclusion principle).

As for how many and what type of fermions and bosons were created at the early universe that has to do with the mechanisms of inflation and reheating processes.

getting higgs theory into the picture, i think that higgs field has something more to do than adding the mass, there must some asymmetry before the particle could take their statistical properties but i am unable to find the event that will bring sufficient asymmetry.

 

[nouveau_riche]

Certainly. You can have a positron and an electron which decay into a pair of photons, and you can also have the reverse.

can you give me an example where matter-antimatter anhilation is not involved in producing a boson fron fermions or vice versa
and the boson produced in the process must have some physical properties instead of being an energy packet.

 

[jarod765]

As for what causes symmetry breaking in the standard model at least to my knowledge I don't think there is a specific mechanism that is widely accepted. In supersymmetry the runing of the higgs mass tends toward negative values in a natural way and it is believed that some higher susy theory will be involved in spontaneous symmetry.

 

[arojo]

Hi,

I think your question does not have an easy answer, the raison why bosons and fermions are different is their statistic. From this we get the fermi and bose statistic, which is related to their spin. The Pauli exclusion principle tells us that the wave function of a set of fermions must be antisymmetric and that bosons have symmetric wave functions.
The problem is that to demonstrate this amazing insight Pauli had, it is necessary to use QFT, actually there is a draft of explanation in wikipedia that I like:

According to the spin-statistics theorem, particles with integer spin occupy symmetric quantum states, and particles with half-integer spin occupy antisymmetric states; furthermore, only integer or half-integer values of spin are allowed by the principles of quantum mechanics. In relativistic quantum field theory, the Pauli principle follows from applying a rotation operator in imaginary time to particles of half-integer spin. Since, nonrelativistically, particles can have any statistics and any spin, there is no way to prove a spin-statistics theorem in nonrelativistic quantum mechanics.

Then there is a second question, about how do we see this difference macroscopically and then I would say that the most spectacular effect is the Bose-Einstein condensate. Other difference are more subtle like what happens when a fermion interacts with a boson (eg the Higgs mechanism).

Finally, you ask if we can transform bosons into fermions and vice-versa, and eventually, if I understood correctly your question is which of both is more fundamental. I am not sure that there is a positive answer for that, what I think we can say is that all the experimental results show a Universe made of boson and fermions (Standard Model) and if this model is the correct one then both fermion and bosons are fundamental.

Cheers

 

[nouveau_riche]

Hi,

I think your question does not have an easy answer, the raison why bosons and fermions are different is their statistic. From this we get the fermi and bose statistic, which is related to their spin. The Pauli exclusion principle tells us that the wave function of a set of fermions must be antisymmetric and that bosons have symmetric wave functions.
The problem is that to demonstrate this amazing insight Pauli had, it is necessary to use QFT, actually there is a draft of explanation in wikipedia that I like:



Then there is a second question, about how do we see this difference macroscopically and then I would say that the most spectacular effect is the Bose-Einstein condensate. Other difference are more subtle like what happens when a fermion interacts with a boson (eg the Higgs mechanism).

Finally, you ask if we can transform bosons into fermions and vice-versa, and eventually, if I understood correctly your question is which of both is more fundamental. I am not sure that there is a positive answer for that, what I think we can say is that all the experimental results show a Universe made of boson and fermions (Standard Model) and if this model is the correct one then both fermion and bosons are fundamental.

Cheers

i read a article when the LHC announced the foundings for higgs boson that just after the big bang the particles were shapeless, without any physical properties and then they interact with higgs field to gain mass and shape. i don't know how this shapeless particle came in the picture.

 

[Simon Bridge]

let me phrase it in the way physics would like

In the early stages of universe, just after the big bang at the moment when particles start to get their properties and dimensions how it is that a particle will become a Fermion or a boson?

That is a good question which nobody knows the answer to. There are some guesses ... the area is work in progress.

We can speculate of course - but that would not be allowed in the forums.
Basically that is just how the Universe is.

I think we missed one:

how do we macroscopically see the effects of bosons

Whole atoms can behave like bosons ... see liquid He II for example.

http://en.wikipedia.org/wiki/Superfluidity

At higher temperatures you can observe the different effects of Bosons and Fermions statistically. Very macroscopically, you need only look to neutron (boson) stars vs White dwarf (fermion) stars.

So did you have a particular effect in mind?

Is there a specific aim to these questions or are you just curious?

 

[nouveau_riche]

That is a good question which nobody knows the answer to. There are some guesses ... the area is work in progress.

We can speculate of course - but that would not be allowed in the forums.
Basically that is just how the Universe is.

I think we missed one:
Whole atoms can behave like bosons ... see liquid He II for example.

http://en.wikipedia.org/wiki/Superfluidity

At higher temperatures you can observe the different effects of Bosons and Fermions statistically. Very macroscopically, you need only look to neutron (boson) stars vs White dwarf (fermion) stars.

So did you have a particular effect in mind?

Is there a specific aim to these questions or are you just curious?

i am not sure but i think the expansion of the universe and the higgs field have something in common to create asymmetries that could explain the action

 

[arojo]

i read a article when the LHC announced the foundings for higgs boson that just after the big bang the particles were shapeless, without any physical properties and then they interact with higgs field to gain mass and shape. i don't know how this shapeless particle came in the picture.

Actually I am not a supporter of the High Energy Physics (HEP) but when comment results we have to be a little bit more objective and to comment the technicalities of the problem we should be more formal about the physics and mathematics behind it.
I am not going to explain in full detail how it works the Higgs mechanism, for that a short comment will not be enough, instead of that you can find a large literature of excellent quality on the web (arxiv is a good site and for free).

My point about mentioning the higgs mechanism, is the fact that as in superconductivity or superfluidity, the interaction with boson is essential. I am pointing this out because you were asking which are the difference between both. It does not matter if the higgs boson exists or not to make this point, the fact that many fermions can interact with boson all of them in the same state is the essential. Which if you look in detail gives some linear dependence that allow the this phenomena to happen.

Cheers

 

[Dale]

can you give me an example where matter-antimatter anhilation is not involved in producing a boson fron fermions

Certainly, emission of photons from an atom returning to the ground state from an excited state is an example of producing a boson from fermions without any anhilation.

and the boson produced in the process must have some physical properties instead of being an energy packet.

The bosons produced must always conserve all conserved quantities, not just energy. For example, spin must also be conserved.

 

[nouveau_riche]

Certainly, emission of photons from an atom returning to the ground state from an excited state is an example of producing a boson from fermions without any anhilation.

The bosons produced must always conserve all conserved quantities, not just energy. For example, spin must also be conserved.

can a boson have charge?

 

[nouveau_riche]

Certainly, emission of photons from an atom returning to the ground state from an excited state is an example of producing a boson from fermions without any anhilation.

the example you are giving me doesn't transform a fermion into a boson it instead produces a boson from its energy.

 

[jtbell]

can a boson have charge?

W+ and W-, for example.

 

[mpv_plate]

...the boson produced in the process must have some physical properties instead of being an energy packet.

A photon produced in annihilation is not just a packet of energy. Photon is a full-fledged particle with physical properties (like the spin, momentum). There is no reason to treat photons as inferior to other particles.

 

[Dale]

the example you are giving me doesn't transform a fermion into a boson it instead produces a boson from its energy.

Ah, I misunderstood, to me "transform" doesn't mean the same as "produce".

As far as I am aware there is no particle reaction which has as inputs only fermions and as outputs only bosons other than matter-antimatter annihilation. However, I am not a particle physicist, so there may be some of which I am not aware.

 

[nouveau_riche]

W+ and W-, for example.

so i would come at the same question again...
an example where a fermion can transform into boson giving him charge, momentum and energy?

 

[Dale]

Why don't matter-antimatter anhilation reactions count?

 

[nouveau_riche]

Why don't matter-antimatter anhilation reactions count?

because i want to see a process where a fermion can modulate its intrinsic physical property that not just involves energy/momentum conservation but its field behavior

 

[Dickfore]

But the statistics an elementary or composite particle obeys is intimately connected to the intrinsic spin of the particle, as given by the Spin-Statistics Theorem.

So if you want to change a fermion into a boson, you would have to change its spin, thus making it a new particle.

There is a kind of a "loophole" with composite particles. Take He-4, for example. It has 2 protons, 2 electrons and 2 neutrons. All of these are fermions. But, when paired, they have integer spin, thus making the nucleus, and the atom of this isotope a boson. In fact, He-4 is the first substance that exhibited superfluid transition.

 

[nouveau_riche]

But the statistics an elementary or composite particle obeys is intimately connected to the intrinsic spin of the particle, as given by the Spin-Statistics Theorem.

So if you want to change a fermion into a boson, you would have to change its spin, thus making it a new particle.

There is a kind of a "loophole" with composite particles. Take He-4, for example. It has 2 protons, 2 electrons and 2 neutrons. All of these are fermions. But, when paired, they have integer spin, thus making the nucleus, and the atom of this isotope a boson. In fact, He-4 is the first substance that exhibited superfluid transition.

it is not just the pairing, they have to be cooled so as to make them superfluid

 

[Dickfore]

Of course. However, being a boson is a necessary condition. He-3, when cooled to the same conditions does not become superfluid.

 

[Dale]

because i want to see a process where a fermion can modulate its intrinsic physical property that not just involves energy/momentum conservation but its field behavior

What do you mean by field behavior?

 

[nouveau_riche]

What do you mean by field behavior?

is it necessary that the bosons will always play the role of force carrier?

 

[Dickfore]

What do you mean by field behavior?

is it necessary that the bosons will always play the role of force carrier?

Why do you answer questions with questions?

 

[nouveau_riche]

Why do you answer questions with questions?

i haven't answer the question yet but i need the answer before i can answer else you will be standing upright with your point

 

[Dale]

is it necessary that the bosons will always play the role of force carrier?

Yes. More specifically, the forces of the standard model are described by gauge fields, and the quanta of those gauge fields are the gauge bosons. Each gauge field's gauge bosons are the carriers of the respective forces. Note that there are other non-gauge bosons which are not excitations of any of the gauge fields and therefore are not carriers of any of the corresponding forces.

 

[Ilmrak]

why is that at relatively low temperature bosons can occupy the same state while the fermions cannot?
and how does we macroscopically see the effects of bosons (with explanations)?

a theoretical answer is preferable

By definition fermion fields creation and destruction operators satisfies

<br /> \{a_\alpha^\dagger, a_\beta^\dagger\}= 0\; , \\<br /> \{a_\alpha,a_\beta\}= 0\; ,\\<br /> \{a_\alpha^\dagger, a_\beta\}= \delta_{\alpha,\beta} \; ,<br />

while boson fields creation and destruction operators satisfies

<br /> \left[a_\alpha^\dagger, a_\beta^\dagger\right]= 0\; ,\\<br /> \left[a_\alpha,a_\beta\right]= 0\; ,\\<br /> \left[ a_\alpha^\dagger, a_\beta\right]= \delta_{\alpha,\beta}\; .<br />

These (anti-)commutation rules implies that two fermions can't be in the same state (a_\alpha^\dagger a_\alpha^\dagger= 0) while two bosons can (a_\alpha^\dagger a_\alpha^\dagger \neq 0).

It can be shown that either a particle is a boson or it's a fermion, there isn't a third option.

Furthermore the Spin-Statistic theorem states that a particle with integer spin has to be a boson, while a semi-odd spin particle has to be a fermion.

Macroscopically a system of bosons can show superfluidity, while maybe the most known examples of the Fermi statistic are neutron stars.

[...] Very macroscopically, you need only look to neutron (boson) stars vs White dwarf (fermion) stars.[...]

Neutrons are fermions!

getting higgs theory into the picture, i think that higgs field has something more to do than adding the mass, there must some asymmetry before the particle could take their statistical properties but i am unable to find the event that will bring sufficient asymmetry.

There's really no need to invoke the Higgs field to explain how particles gains their statistical properties.
Actually your sentence sounds as a non-sense, as the Higgs is a boson (spin zero) and so statistics is needed to describe even the Higgs field.
Note that Fermi and Bose statistics reflects symmetries, not asymmetries.

can you give me an example where matter-antimatter anhilation is not involved in producing a boson fron fermions or vice versa
and the boson produced in the process must have some physical properties instead of being an energy packet.

All bosons has physical properties.
However, a process you may like is

e^- \;\bar{\nu}_e \rightarrow W^- \; ,

where e^- and \bar{\nu}_e are fermions and W^- is a boson.

is it necessary that the bosons will always play the role of force carrier?

No it's not necessary.
In the standard model there is exactly one boson that is not a gauge boson and so doesn't carry a force: the Higgs boson.

I hope this could help a bit.

Ilm

 

[mpv_plate]

is it necessary that the bosons will always play the role of force carrier?

Two bosons can scatter of each other thanks to intermediate fermions. That is the case of photon-photon scattering which happens due to interaction via the virtual electron-positron pair. However I am not sure if this is what you asked for.

 

[Simon Bridge]

is it necessary that the bosons will always play the role of force carrier?

No. It is the other way around: in the standard model, the gauge fields give rise to force carriers which are bosons.
Not all interactions need be mediated by bosons.
Not all spin 0 objects are force carriers.

Now please answer the question posed by dalespam: "what do you mean by field behaviour?"

We cannot help you if you will not answer questions.

 

[nouveau_riche]

No. It is the other way around: in the standard model, the gauge fields give rise to force carriers which are bosons.
Not all interactions need be mediated by bosons.
Not all spin 0 objects are force carriers.

Now please answer the question posed by dalespam: "what do you mean by field behaviour?"

We cannot help you if you will not answer questions.

what i meant to say was that if a fermion is changing into a boson that is a carrier of force, the field generating fermion has itself transformed into the carrier under some conditions, this could help to figure the fermion-boson relationship.

 

[Ilmrak]

what i meant to say was that if a fermion is changing into a boson that is a carrier of force, the field generating fermion has itself transformed into the carrier under some conditions, this could help to figure the fermion-boson relationship.

I think it may be worth to remark that the bosonic or fermionic nature of a field is a symmetry property of that field. A field would have such a symmetry even if it was the only field of your theory, it doesn't depend on the other fields and in particular it doesn't depend on the interaction with other particles.

So I think you should change a bit your perspective on this topic, maybe trying to formulate different kind of questions to better understand bosons and fermions.

Ilm