Why do bosons tend to occupy the same state?Can bosons that are composed of several fermions occupy the same state?What prevents bosons from occupying the same location?Fermions in the same stateAlmost identical fermions fighting for the same stateDoes gravity limit the number of bosons that can occupy the same single-particle state?Why are composite fermions either bosons or fermions but not neither?What is the physical (i.e. non-mathematical) cause off the difference between a system of identical bosons and fermions?Can two fermions occupy the same energy level in infinite potential well?Why is a collection of non-interacting bosons pathological?Why do composite bosons form a BEC?
What do three bars across the stem of a note mean?
How can I prevent hyper evolved versions of regular creatures from wiping out their cousins?
Today is the Center
LaTeX closing $ signs makes cursor jump
Email Account under attack (really) - anything I can do?
How did the USSR manage to innovate in an environment characterized by government censorship and high bureaucracy?
Why do falling prices hurt debtors?
Why was the small council so happy for Tyrion to become the Master of Coin?
How to find program name(s) of an installed package?
Dragon forelimb placement
Why is consensus so controversial in Britain?
Collect Fourier series terms
In Japanese, what’s the difference between “Tonari ni” (となりに) and “Tsugi” (つぎ)? When would you use one over the other?
Why can't I see bouncing of a switch on an oscilloscope?
What do the dots in this tr command do: tr .............A-Z A-ZA-Z <<< "JVPQBOV" (with 13 dots)
Can an x86 CPU running in real mode be considered to be basically an 8086 CPU?
Can divisibility rules for digits be generalized to sum of digits
Languages that we cannot (dis)prove to be Context-Free
Can I ask the recruiters in my resume to put the reason why I am rejected?
What's the point of deactivating Num Lock on login screens?
Theorems that impeded progress
Why are 150k or 200k jobs considered good when there are 300k+ births a month?
Have astronauts in space suits ever taken selfies? If so, how?
Smoothness of finite-dimensional functional calculus
Why do bosons tend to occupy the same state?
Can bosons that are composed of several fermions occupy the same state?What prevents bosons from occupying the same location?Fermions in the same stateAlmost identical fermions fighting for the same stateDoes gravity limit the number of bosons that can occupy the same single-particle state?Why are composite fermions either bosons or fermions but not neither?What is the physical (i.e. non-mathematical) cause off the difference between a system of identical bosons and fermions?Can two fermions occupy the same energy level in infinite potential well?Why is a collection of non-interacting bosons pathological?Why do composite bosons form a BEC?
$begingroup$
It is often said that, while many fermions cannot occupy the same state, bosons have the tendency to do that. Sometimes this is expressed figuratively by saying, for example, that "bosons are sociable" or that "bosons want to stay as close as possible".
I understand that the symmetry of the wavefunction allows many bosons to be in the same one-particle state, but I can't see why they should prefer to do that rather than occupying different states.
Anyway, according to many science writers, bosons not only can be in the same state, but they also tend to do that. Why is it like that?
quantum-mechanics bosons quantum-statistics
edited 2 days ago
knzhou
46.5k11125224
asked Apr 3 at 14:45
HicHaecHocHicHaecHoc
1338
$endgroup$
add a comment |
$begingroup$
It is often said that, while many fermions cannot occupy the same state, bosons have the tendency to do that. Sometimes this is expressed figuratively by saying, for example, that "bosons are sociable" or that "bosons want to stay as close as possible".
I understand that the symmetry of the wavefunction allows many bosons to be in the same one-particle state, but I can't see why they should prefer to do that rather than occupying different states.
Anyway, according to many science writers, bosons not only can be in the same state, but they also tend to do that. Why is it like that?
quantum-mechanics bosons quantum-statistics
edited 2 days ago
knzhou
46.5k11125224
asked Apr 3 at 14:45
HicHaecHocHicHaecHoc
1338
$endgroup$
add a comment |
$begingroup$
It is often said that, while many fermions cannot occupy the same state, bosons have the tendency to do that. Sometimes this is expressed figuratively by saying, for example, that "bosons are sociable" or that "bosons want to stay as close as possible".
I understand that the symmetry of the wavefunction allows many bosons to be in the same one-particle state, but I can't see why they should prefer to do that rather than occupying different states.
Anyway, according to many science writers, bosons not only can be in the same state, but they also tend to do that. Why is it like that?
quantum-mechanics bosons quantum-statistics
edited 2 days ago
knzhou
46.5k11125224
asked Apr 3 at 14:45
HicHaecHocHicHaecHoc
1338
$endgroup$
It is often said that, while many fermions cannot occupy the same state, bosons have the tendency to do that. Sometimes this is expressed figuratively by saying, for example, that "bosons are sociable" or that "bosons want to stay as close as possible".
I understand that the symmetry of the wavefunction allows many bosons to be in the same one-particle state, but I can't see why they should prefer to do that rather than occupying different states.
Anyway, according to many science writers, bosons not only can be in the same state, but they also tend to do that. Why is it like that?
quantum-mechanics bosons quantum-statistics
quantum-mechanics bosons quantum-statistics
edited 2 days ago
knzhou
46.5k11125224
asked Apr 3 at 14:45
HicHaecHocHicHaecHoc
1338
edited 2 days ago
knzhou
46.5k11125224
asked Apr 3 at 14:45
HicHaecHocHicHaecHoc
1338
edited 2 days ago
knzhou
46.5k11125224
edited 2 days ago
knzhou
46.5k11125224
edited 2 days ago
knzhou
46.5k11125224
46.5k11125224
asked Apr 3 at 14:45
HicHaecHocHicHaecHoc
1338
asked Apr 3 at 14:45
HicHaecHocHicHaecHoc
1338
asked Apr 3 at 14:45
HicHaecHocHicHaecHoc
1338
1338
add a comment |
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
Suppose you have two distinguishable coins that can either come up heads or tails. Then there are four equally likely possibilities,
$$textHH, textHT, textTH, textTT.$$
There is a 50% chance for the two coins to have the same result.
If the coins were fermions and "heads/tails" were quantum modes, the $textHH$ and $textTT$ states wouldn't be allowed, so there is a 0% chance for the two coins to have the same result.
If the coins were bosons, then all states are allowed. But there's a twist: bosons are identical particles. The states $textHT$ and $textTH$ are precisely the same state, namely the one with one particle in each of the two modes. So there are three possibilities,
$$texttwo heads, texttwo tails, textone each$$
and hence in the microcanonical ensemble (where each distinct quantum state is equally probable) there is a $2/3$ chance of double occupancy, not $1/2$. That's what people mean when they say bosons "clump up", though it's not really a consequence of bosonic statistics, just a consequence of the particles being identical. Whenever a system of bosonic particles is in thermal equilibrium, there exist fewer states with the bosons apart than you would naively expect, if you treated them as distinguishable particles, so you are more likely to see them together.
answered Apr 3 at 15:08
knzhouknzhou
46.5k11125224
$endgroup$
2
$begingroup$
@HicHaecHoc The statement is not that any two bosons are more than 50% likely to be in the same state, it's that you get more clumping with bosons than with distinguishable particles when you average over all states.
$endgroup$
– knzhou
Apr 3 at 15:27
5
$begingroup$
@HicHaecHoc Popularization is always like that. I think virtual particles are even more misleading, but when my well-intentioned little sister (with zero physics background) wants to know what I'm studying, you better bet I'm weaving a fantastic tale of how virtual particles crash into each other.
$endgroup$
– knzhou
Apr 3 at 16:41
3
$begingroup$
In coming up with the 2/3 value you make a logical leap in assuming equiprobability of events. It's sort of along the same lines as "Either Bill Gates will give me a million dollars tonight or he won't. Therefore, there's a 50% chance I'll be a millionaire tomorrow!" Now, in this particular case equiprobability of the three states may be correct (versus "one each" being twice as likely as either of the others), but the answer could be improved by more directly addressing it, rather treating it in a fashion which normally would be a probabilistic fallacy.
$endgroup$
– R.M.
Apr 3 at 22:16
2
$begingroup$
@R.M. I said "in the microcanonical ensemble", which is precisely the assumption that the states are equally likely. (This is what happens when you give the system a fixed energy and let it come to thermal equilibrium.) But yeah, it's true I didn't justify why that happens -- it's kind of the fundamental postulate that makes all of our reasoning about thermal physics work, so it would be a whole book to say anything more! You could phrase it other ways, but I preferred talking about a thermodynamic example because it makes it easier to connect to the probabilities I had above.
$endgroup$
– knzhou
2 days ago
3
$begingroup$
@gented No, the Hilbert space is 3-dimensional and not 4-dimensional. It's the symmetrized tensor product, not the ordinary tensor product. "Indistinguishable" has a deeper meaning than just being indistinguishable in practice.
$endgroup$
– knzhou
2 days ago
|
show 14 more comments
$begingroup$
Anyway, according to many science writers, bosons not only can be in the same state, but they also tend to do that. Why is it like that?
That's simply wrong. It's one of many clichés dear to popular science writers but with little physical content. What's true, as you said, is that bosons can occupy the same state, as opposed to fermions. As to tendency, it has the same half-truth as when one says "a system tends
to stay in its ground state".
In fact assume the latter statement is inconditionally true and you have an ensemble of non-interacting bosons. Then each boson will tend to occupy its ground state and - since nothing forbids that - all particles will sit there. In presence of interaction things may go different or not depending on the interaction.
But the real issue is if there is the tendency of a system to stay in its ground state or go into it if initially placed in a state of higher energy. However this is a question not easy to deal with in few words.
answered Apr 3 at 15:15
Elio FabriElio Fabri
3,5451214
$endgroup$
1
$begingroup$
No, bosons do actually 'clump' relative to classical Maxwell-Boltzmann particles, at least under some circumstances. A nice example is the Hong-Ou-Mandel effect: en.wikipedia.org/wiki/Hong%E2%80%93Ou%E2%80%93Mandel_effect
$endgroup$
– Rococo
Apr 3 at 15:49
add a comment |
Your Answer
StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
);
);
, "mathjax-editing");
StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "151"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);
StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);
else
createEditor();
);
function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);
);
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fphysics.stackexchange.com%2fquestions%2f470316%2fwhy-do-bosons-tend-to-occupy-the-same-state%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
2 Answers
2
active
oldest
votes
2 Answers
2
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
Suppose you have two distinguishable coins that can either come up heads or tails. Then there are four equally likely possibilities,
$$textHH, textHT, textTH, textTT.$$
There is a 50% chance for the two coins to have the same result.
If the coins were fermions and "heads/tails" were quantum modes, the $textHH$ and $textTT$ states wouldn't be allowed, so there is a 0% chance for the two coins to have the same result.
If the coins were bosons, then all states are allowed. But there's a twist: bosons are identical particles. The states $textHT$ and $textTH$ are precisely the same state, namely the one with one particle in each of the two modes. So there are three possibilities,
$$texttwo heads, texttwo tails, textone each$$
and hence in the microcanonical ensemble (where each distinct quantum state is equally probable) there is a $2/3$ chance of double occupancy, not $1/2$. That's what people mean when they say bosons "clump up", though it's not really a consequence of bosonic statistics, just a consequence of the particles being identical. Whenever a system of bosonic particles is in thermal equilibrium, there exist fewer states with the bosons apart than you would naively expect, if you treated them as distinguishable particles, so you are more likely to see them together.
answered Apr 3 at 15:08
knzhouknzhou
46.5k11125224
$endgroup$
2
$begingroup$
@HicHaecHoc The statement is not that any two bosons are more than 50% likely to be in the same state, it's that you get more clumping with bosons than with distinguishable particles when you average over all states.
$endgroup$
– knzhou
Apr 3 at 15:27
5
$begingroup$
@HicHaecHoc Popularization is always like that. I think virtual particles are even more misleading, but when my well-intentioned little sister (with zero physics background) wants to know what I'm studying, you better bet I'm weaving a fantastic tale of how virtual particles crash into each other.
$endgroup$
– knzhou
Apr 3 at 16:41
3
$begingroup$
In coming up with the 2/3 value you make a logical leap in assuming equiprobability of events. It's sort of along the same lines as "Either Bill Gates will give me a million dollars tonight or he won't. Therefore, there's a 50% chance I'll be a millionaire tomorrow!" Now, in this particular case equiprobability of the three states may be correct (versus "one each" being twice as likely as either of the others), but the answer could be improved by more directly addressing it, rather treating it in a fashion which normally would be a probabilistic fallacy.
$endgroup$
– R.M.
Apr 3 at 22:16
2
$begingroup$
@R.M. I said "in the microcanonical ensemble", which is precisely the assumption that the states are equally likely. (This is what happens when you give the system a fixed energy and let it come to thermal equilibrium.) But yeah, it's true I didn't justify why that happens -- it's kind of the fundamental postulate that makes all of our reasoning about thermal physics work, so it would be a whole book to say anything more! You could phrase it other ways, but I preferred talking about a thermodynamic example because it makes it easier to connect to the probabilities I had above.
$endgroup$
– knzhou
2 days ago
3
$begingroup$
@gented No, the Hilbert space is 3-dimensional and not 4-dimensional. It's the symmetrized tensor product, not the ordinary tensor product. "Indistinguishable" has a deeper meaning than just being indistinguishable in practice.
$endgroup$
– knzhou
2 days ago
|
show 14 more comments
$begingroup$
Suppose you have two distinguishable coins that can either come up heads or tails. Then there are four equally likely possibilities,
$$textHH, textHT, textTH, textTT.$$
There is a 50% chance for the two coins to have the same result.
If the coins were fermions and "heads/tails" were quantum modes, the $textHH$ and $textTT$ states wouldn't be allowed, so there is a 0% chance for the two coins to have the same result.
If the coins were bosons, then all states are allowed. But there's a twist: bosons are identical particles. The states $textHT$ and $textTH$ are precisely the same state, namely the one with one particle in each of the two modes. So there are three possibilities,
$$texttwo heads, texttwo tails, textone each$$
and hence in the microcanonical ensemble (where each distinct quantum state is equally probable) there is a $2/3$ chance of double occupancy, not $1/2$. That's what people mean when they say bosons "clump up", though it's not really a consequence of bosonic statistics, just a consequence of the particles being identical. Whenever a system of bosonic particles is in thermal equilibrium, there exist fewer states with the bosons apart than you would naively expect, if you treated them as distinguishable particles, so you are more likely to see them together.
answered Apr 3 at 15:08
knzhouknzhou
46.5k11125224
$endgroup$
2
$begingroup$
@HicHaecHoc The statement is not that any two bosons are more than 50% likely to be in the same state, it's that you get more clumping with bosons than with distinguishable particles when you average over all states.
$endgroup$
– knzhou
Apr 3 at 15:27
5
$begingroup$
@HicHaecHoc Popularization is always like that. I think virtual particles are even more misleading, but when my well-intentioned little sister (with zero physics background) wants to know what I'm studying, you better bet I'm weaving a fantastic tale of how virtual particles crash into each other.
$endgroup$
– knzhou
Apr 3 at 16:41
3
$begingroup$
In coming up with the 2/3 value you make a logical leap in assuming equiprobability of events. It's sort of along the same lines as "Either Bill Gates will give me a million dollars tonight or he won't. Therefore, there's a 50% chance I'll be a millionaire tomorrow!" Now, in this particular case equiprobability of the three states may be correct (versus "one each" being twice as likely as either of the others), but the answer could be improved by more directly addressing it, rather treating it in a fashion which normally would be a probabilistic fallacy.
$endgroup$
– R.M.
Apr 3 at 22:16
2
$begingroup$
@R.M. I said "in the microcanonical ensemble", which is precisely the assumption that the states are equally likely. (This is what happens when you give the system a fixed energy and let it come to thermal equilibrium.) But yeah, it's true I didn't justify why that happens -- it's kind of the fundamental postulate that makes all of our reasoning about thermal physics work, so it would be a whole book to say anything more! You could phrase it other ways, but I preferred talking about a thermodynamic example because it makes it easier to connect to the probabilities I had above.
$endgroup$
– knzhou
2 days ago
3
$begingroup$
@gented No, the Hilbert space is 3-dimensional and not 4-dimensional. It's the symmetrized tensor product, not the ordinary tensor product. "Indistinguishable" has a deeper meaning than just being indistinguishable in practice.
$endgroup$
– knzhou
2 days ago
|
show 14 more comments
$begingroup$
Suppose you have two distinguishable coins that can either come up heads or tails. Then there are four equally likely possibilities,
$$textHH, textHT, textTH, textTT.$$
There is a 50% chance for the two coins to have the same result.
If the coins were fermions and "heads/tails" were quantum modes, the $textHH$ and $textTT$ states wouldn't be allowed, so there is a 0% chance for the two coins to have the same result.
If the coins were bosons, then all states are allowed. But there's a twist: bosons are identical particles. The states $textHT$ and $textTH$ are precisely the same state, namely the one with one particle in each of the two modes. So there are three possibilities,
$$texttwo heads, texttwo tails, textone each$$
and hence in the microcanonical ensemble (where each distinct quantum state is equally probable) there is a $2/3$ chance of double occupancy, not $1/2$. That's what people mean when they say bosons "clump up", though it's not really a consequence of bosonic statistics, just a consequence of the particles being identical. Whenever a system of bosonic particles is in thermal equilibrium, there exist fewer states with the bosons apart than you would naively expect, if you treated them as distinguishable particles, so you are more likely to see them together.
answered Apr 3 at 15:08
knzhouknzhou
46.5k11125224
$endgroup$
Suppose you have two distinguishable coins that can either come up heads or tails. Then there are four equally likely possibilities,
$$textHH, textHT, textTH, textTT.$$
There is a 50% chance for the two coins to have the same result.
If the coins were fermions and "heads/tails" were quantum modes, the $textHH$ and $textTT$ states wouldn't be allowed, so there is a 0% chance for the two coins to have the same result.
If the coins were bosons, then all states are allowed. But there's a twist: bosons are identical particles. The states $textHT$ and $textTH$ are precisely the same state, namely the one with one particle in each of the two modes. So there are three possibilities,
$$texttwo heads, texttwo tails, textone each$$
and hence in the microcanonical ensemble (where each distinct quantum state is equally probable) there is a $2/3$ chance of double occupancy, not $1/2$. That's what people mean when they say bosons "clump up", though it's not really a consequence of bosonic statistics, just a consequence of the particles being identical. Whenever a system of bosonic particles is in thermal equilibrium, there exist fewer states with the bosons apart than you would naively expect, if you treated them as distinguishable particles, so you are more likely to see them together.
answered Apr 3 at 15:08
knzhouknzhou
46.5k11125224
edited 2 days ago
answered Apr 3 at 15:08
knzhouknzhou
46.5k11125224
answered Apr 3 at 15:08
knzhouknzhou
46.5k11125224
answered Apr 3 at 15:08
knzhouknzhou
46.5k11125224
46.5k11125224
2
$begingroup$
@HicHaecHoc The statement is not that any two bosons are more than 50% likely to be in the same state, it's that you get more clumping with bosons than with distinguishable particles when you average over all states.
$endgroup$
– knzhou
Apr 3 at 15:27
5
$begingroup$
@HicHaecHoc Popularization is always like that. I think virtual particles are even more misleading, but when my well-intentioned little sister (with zero physics background) wants to know what I'm studying, you better bet I'm weaving a fantastic tale of how virtual particles crash into each other.
$endgroup$
– knzhou
Apr 3 at 16:41
3
$begingroup$
In coming up with the 2/3 value you make a logical leap in assuming equiprobability of events. It's sort of along the same lines as "Either Bill Gates will give me a million dollars tonight or he won't. Therefore, there's a 50% chance I'll be a millionaire tomorrow!" Now, in this particular case equiprobability of the three states may be correct (versus "one each" being twice as likely as either of the others), but the answer could be improved by more directly addressing it, rather treating it in a fashion which normally would be a probabilistic fallacy.
$endgroup$
– R.M.
Apr 3 at 22:16
2
$begingroup$
@R.M. I said "in the microcanonical ensemble", which is precisely the assumption that the states are equally likely. (This is what happens when you give the system a fixed energy and let it come to thermal equilibrium.) But yeah, it's true I didn't justify why that happens -- it's kind of the fundamental postulate that makes all of our reasoning about thermal physics work, so it would be a whole book to say anything more! You could phrase it other ways, but I preferred talking about a thermodynamic example because it makes it easier to connect to the probabilities I had above.
$endgroup$
– knzhou
2 days ago
3
$begingroup$
@gented No, the Hilbert space is 3-dimensional and not 4-dimensional. It's the symmetrized tensor product, not the ordinary tensor product. "Indistinguishable" has a deeper meaning than just being indistinguishable in practice.
$endgroup$
– knzhou
2 days ago
|
show 14 more comments
2
$begingroup$
@HicHaecHoc The statement is not that any two bosons are more than 50% likely to be in the same state, it's that you get more clumping with bosons than with distinguishable particles when you average over all states.
$endgroup$
– knzhou
Apr 3 at 15:27
5
$begingroup$
@HicHaecHoc Popularization is always like that. I think virtual particles are even more misleading, but when my well-intentioned little sister (with zero physics background) wants to know what I'm studying, you better bet I'm weaving a fantastic tale of how virtual particles crash into each other.
$endgroup$
– knzhou
Apr 3 at 16:41
3
$begingroup$
In coming up with the 2/3 value you make a logical leap in assuming equiprobability of events. It's sort of along the same lines as "Either Bill Gates will give me a million dollars tonight or he won't. Therefore, there's a 50% chance I'll be a millionaire tomorrow!" Now, in this particular case equiprobability of the three states may be correct (versus "one each" being twice as likely as either of the others), but the answer could be improved by more directly addressing it, rather treating it in a fashion which normally would be a probabilistic fallacy.
$endgroup$
– R.M.
Apr 3 at 22:16
2
$begingroup$
@R.M. I said "in the microcanonical ensemble", which is precisely the assumption that the states are equally likely. (This is what happens when you give the system a fixed energy and let it come to thermal equilibrium.) But yeah, it's true I didn't justify why that happens -- it's kind of the fundamental postulate that makes all of our reasoning about thermal physics work, so it would be a whole book to say anything more! You could phrase it other ways, but I preferred talking about a thermodynamic example because it makes it easier to connect to the probabilities I had above.
$endgroup$
– knzhou
2 days ago
3
$begingroup$
@gented No, the Hilbert space is 3-dimensional and not 4-dimensional. It's the symmetrized tensor product, not the ordinary tensor product. "Indistinguishable" has a deeper meaning than just being indistinguishable in practice.
$endgroup$
– knzhou
2 days ago
2
2
$begingroup$
@HicHaecHoc The statement is not that any two bosons are more than 50% likely to be in the same state, it's that you get more clumping with bosons than with distinguishable particles when you average over all states.
$endgroup$
– knzhou
Apr 3 at 15:27
$begingroup$
@HicHaecHoc The statement is not that any two bosons are more than 50% likely to be in the same state, it's that you get more clumping with bosons than with distinguishable particles when you average over all states.
$endgroup$
– knzhou
Apr 3 at 15:27
5
5
$begingroup$
@HicHaecHoc Popularization is always like that. I think virtual particles are even more misleading, but when my well-intentioned little sister (with zero physics background) wants to know what I'm studying, you better bet I'm weaving a fantastic tale of how virtual particles crash into each other.
$endgroup$
– knzhou
Apr 3 at 16:41
$begingroup$
@HicHaecHoc Popularization is always like that. I think virtual particles are even more misleading, but when my well-intentioned little sister (with zero physics background) wants to know what I'm studying, you better bet I'm weaving a fantastic tale of how virtual particles crash into each other.
$endgroup$
– knzhou
Apr 3 at 16:41
3
3
$begingroup$
In coming up with the 2/3 value you make a logical leap in assuming equiprobability of events. It's sort of along the same lines as "Either Bill Gates will give me a million dollars tonight or he won't. Therefore, there's a 50% chance I'll be a millionaire tomorrow!" Now, in this particular case equiprobability of the three states may be correct (versus "one each" being twice as likely as either of the others), but the answer could be improved by more directly addressing it, rather treating it in a fashion which normally would be a probabilistic fallacy.
$endgroup$
– R.M.
Apr 3 at 22:16
$begingroup$
In coming up with the 2/3 value you make a logical leap in assuming equiprobability of events. It's sort of along the same lines as "Either Bill Gates will give me a million dollars tonight or he won't. Therefore, there's a 50% chance I'll be a millionaire tomorrow!" Now, in this particular case equiprobability of the three states may be correct (versus "one each" being twice as likely as either of the others), but the answer could be improved by more directly addressing it, rather treating it in a fashion which normally would be a probabilistic fallacy.
$endgroup$
– R.M.
Apr 3 at 22:16
2
2
$begingroup$
@R.M. I said "in the microcanonical ensemble", which is precisely the assumption that the states are equally likely. (This is what happens when you give the system a fixed energy and let it come to thermal equilibrium.) But yeah, it's true I didn't justify why that happens -- it's kind of the fundamental postulate that makes all of our reasoning about thermal physics work, so it would be a whole book to say anything more! You could phrase it other ways, but I preferred talking about a thermodynamic example because it makes it easier to connect to the probabilities I had above.
$endgroup$
– knzhou
2 days ago
$begingroup$
@R.M. I said "in the microcanonical ensemble", which is precisely the assumption that the states are equally likely. (This is what happens when you give the system a fixed energy and let it come to thermal equilibrium.) But yeah, it's true I didn't justify why that happens -- it's kind of the fundamental postulate that makes all of our reasoning about thermal physics work, so it would be a whole book to say anything more! You could phrase it other ways, but I preferred talking about a thermodynamic example because it makes it easier to connect to the probabilities I had above.
$endgroup$
– knzhou
2 days ago
3
3
$begingroup$
@gented No, the Hilbert space is 3-dimensional and not 4-dimensional. It's the symmetrized tensor product, not the ordinary tensor product. "Indistinguishable" has a deeper meaning than just being indistinguishable in practice.
$endgroup$
– knzhou
2 days ago
$begingroup$
@gented No, the Hilbert space is 3-dimensional and not 4-dimensional. It's the symmetrized tensor product, not the ordinary tensor product. "Indistinguishable" has a deeper meaning than just being indistinguishable in practice.
$endgroup$
– knzhou
2 days ago
|
show 14 more comments
$begingroup$
Anyway, according to many science writers, bosons not only can be in the same state, but they also tend to do that. Why is it like that?
That's simply wrong. It's one of many clichés dear to popular science writers but with little physical content. What's true, as you said, is that bosons can occupy the same state, as opposed to fermions. As to tendency, it has the same half-truth as when one says "a system tends
to stay in its ground state".
In fact assume the latter statement is inconditionally true and you have an ensemble of non-interacting bosons. Then each boson will tend to occupy its ground state and - since nothing forbids that - all particles will sit there. In presence of interaction things may go different or not depending on the interaction.
But the real issue is if there is the tendency of a system to stay in its ground state or go into it if initially placed in a state of higher energy. However this is a question not easy to deal with in few words.
answered Apr 3 at 15:15
Elio FabriElio Fabri
3,5451214
$endgroup$
1
$begingroup$
No, bosons do actually 'clump' relative to classical Maxwell-Boltzmann particles, at least under some circumstances. A nice example is the Hong-Ou-Mandel effect: en.wikipedia.org/wiki/Hong%E2%80%93Ou%E2%80%93Mandel_effect
$endgroup$
– Rococo
Apr 3 at 15:49
add a comment |
$begingroup$
Anyway, according to many science writers, bosons not only can be in the same state, but they also tend to do that. Why is it like that?
That's simply wrong. It's one of many clichés dear to popular science writers but with little physical content. What's true, as you said, is that bosons can occupy the same state, as opposed to fermions. As to tendency, it has the same half-truth as when one says "a system tends
to stay in its ground state".
In fact assume the latter statement is inconditionally true and you have an ensemble of non-interacting bosons. Then each boson will tend to occupy its ground state and - since nothing forbids that - all particles will sit there. In presence of interaction things may go different or not depending on the interaction.
But the real issue is if there is the tendency of a system to stay in its ground state or go into it if initially placed in a state of higher energy. However this is a question not easy to deal with in few words.
answered Apr 3 at 15:15
Elio FabriElio Fabri
3,5451214
$endgroup$
1
$begingroup$
No, bosons do actually 'clump' relative to classical Maxwell-Boltzmann particles, at least under some circumstances. A nice example is the Hong-Ou-Mandel effect: en.wikipedia.org/wiki/Hong%E2%80%93Ou%E2%80%93Mandel_effect
$endgroup$
– Rococo
Apr 3 at 15:49
add a comment |
$begingroup$
Anyway, according to many science writers, bosons not only can be in the same state, but they also tend to do that. Why is it like that?
That's simply wrong. It's one of many clichés dear to popular science writers but with little physical content. What's true, as you said, is that bosons can occupy the same state, as opposed to fermions. As to tendency, it has the same half-truth as when one says "a system tends
to stay in its ground state".
In fact assume the latter statement is inconditionally true and you have an ensemble of non-interacting bosons. Then each boson will tend to occupy its ground state and - since nothing forbids that - all particles will sit there. In presence of interaction things may go different or not depending on the interaction.
But the real issue is if there is the tendency of a system to stay in its ground state or go into it if initially placed in a state of higher energy. However this is a question not easy to deal with in few words.
answered Apr 3 at 15:15
Elio FabriElio Fabri
3,5451214
$endgroup$
Anyway, according to many science writers, bosons not only can be in the same state, but they also tend to do that. Why is it like that?
That's simply wrong. It's one of many clichés dear to popular science writers but with little physical content. What's true, as you said, is that bosons can occupy the same state, as opposed to fermions. As to tendency, it has the same half-truth as when one says "a system tends
to stay in its ground state".
In fact assume the latter statement is inconditionally true and you have an ensemble of non-interacting bosons. Then each boson will tend to occupy its ground state and - since nothing forbids that - all particles will sit there. In presence of interaction things may go different or not depending on the interaction.
But the real issue is if there is the tendency of a system to stay in its ground state or go into it if initially placed in a state of higher energy. However this is a question not easy to deal with in few words.
answered Apr 3 at 15:15
Elio FabriElio Fabri
3,5451214
answered Apr 3 at 15:15
Elio FabriElio Fabri
3,5451214
answered Apr 3 at 15:15
Elio FabriElio Fabri
3,5451214
answered Apr 3 at 15:15
Elio FabriElio Fabri
3,5451214
3,5451214
1
$begingroup$
No, bosons do actually 'clump' relative to classical Maxwell-Boltzmann particles, at least under some circumstances. A nice example is the Hong-Ou-Mandel effect: en.wikipedia.org/wiki/Hong%E2%80%93Ou%E2%80%93Mandel_effect
$endgroup$
– Rococo
Apr 3 at 15:49
add a comment |
1
$begingroup$
No, bosons do actually 'clump' relative to classical Maxwell-Boltzmann particles, at least under some circumstances. A nice example is the Hong-Ou-Mandel effect: en.wikipedia.org/wiki/Hong%E2%80%93Ou%E2%80%93Mandel_effect
$endgroup$
– Rococo
Apr 3 at 15:49
1
1
$begingroup$
No, bosons do actually 'clump' relative to classical Maxwell-Boltzmann particles, at least under some circumstances. A nice example is the Hong-Ou-Mandel effect: en.wikipedia.org/wiki/Hong%E2%80%93Ou%E2%80%93Mandel_effect
$endgroup$
– Rococo
Apr 3 at 15:49
$begingroup$
No, bosons do actually 'clump' relative to classical Maxwell-Boltzmann particles, at least under some circumstances. A nice example is the Hong-Ou-Mandel effect: en.wikipedia.org/wiki/Hong%E2%80%93Ou%E2%80%93Mandel_effect
$endgroup$
– Rococo
Apr 3 at 15:49
add a comment |
Thanks for contributing an answer to Physics Stack Exchange!
- Please be sure to answer the question. Provide details and share your research!
But avoid …
- Asking for help, clarification, or responding to other answers.
- Making statements based on opinion; back them up with references or personal experience.
Use MathJax to format equations. MathJax reference.
To learn more, see our tips on writing great answers.
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fphysics.stackexchange.com%2fquestions%2f470316%2fwhy-do-bosons-tend-to-occupy-the-same-state%23new-answer', 'question_page');
);
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Sign up or log in
StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Sign up using Google
Sign up using Facebook
Sign up using Email and Password
Post as a guest
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
Required, but never shown
