A Volovik vs Witten vs Wen, etc.

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I'd like to ask about models where condense matter physics is used as fundamental feature of nature.
What is the difference between Volovik and Witten model. Is it Volovik using quantum mechanics as more fundamental to QFT? And Witten not claiming it? Compare this with the claims of Hrvoje Nikolic' that QM is more fundamental than QFT (see https://arxiv.org/pdf/1811.11643.pdf). For those familiar with arguments about it. How do they differ? How popular is this condense matter connection thing among Physicists? Please share the views of each major proponent including Wen and others I haven't mentioned. Thank you.

Witten's https://arxiv.org/abs/1710.01791

"Condensed matter physicists are accustomed to such "emergent" phenomena, so to get an idea about the status of symmetries in an emergent description of Nature, we might take a look at what
happens in that field. Global symmetries that emerge in a low energy limit are commonplace in condensed matter physics. But they are always approximate symmetries that are explicitly violated
by operators of higher dimension that are "irrelevant" in the renormalization group sense. Thus the global symmetries in emergent descriptions of condensed matter systems are always analogous to Le 􀀀 L or L 􀀀 L in the Standard Model { or to strangeness, etc., from the point of view of QED or QCD.

By contrast, useful low energy descriptions of condensed matter systems can often have exact gauge symmetries that are "emergent," meaning that they do not have any particular meaning in the microscopic Schrodinger equation for electrons and nuclei. The most familiar example would be the emergent U(1) gauge symmetries that are often used in effective field theories of the fractional quantum Hall effect in 2 + 1 dimensions. These are indeed exact gauge symmetries, not explicitly broken by high dimension operators. Gauge theory with explicit gauge symmetry breaking is not ordinarily a useful concept."
 
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Another thing. At very small scale like planck scale, you need very high energy to probe them (so high we couldn't do it due to engineering limit).

However. If you don't use ordinary particles but exotic ones (corresponding to more fundamental particles that may not have deBroglie wavelength). Can you probe the planck scale?

Let me elaborate. In beyond the standard model such as Nikolic's (and Wen's? or even Witten's) fundamental particles in condense matter analogy. It doesn't necessarily mean high energy particles were required to probe very small scale, or if the fundamental particles were planck size, it doesn't mean it has high energy?

At least just wanting to know in principle if in beyond standard model. It is possible to have very small particles at small scale that doesn't require high energy probes (none-ordinary particles) or way to interact with them.
 

Demystifier

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It doesn't necessarily mean high energy particles were required to probe very small scale, or if the fundamental particles were planck size, it doesn't mean it has high energy?
To probe small spatial distances, one needs large 3-momenta. But if Lorentz invariance is emergent at large distances and not fundamental at small distances, then large 3-momentum does not necessarily need to correspond to a large energy. For instance, if the dispersion relation is something like
$$\omega^2=c_0+c_2{\bf k}^2+c_4{\bf k}^4+...$$
with ##c_0=m^2\geq 0##, ##c_2=1## and ##c_4<0##, then one can have small energy ##\omega## for a sufficiently large momentum ##|{\bf k}|##.
 

Demystifier

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How popular is this condense matter connection thing among Physicists?
Unfortunately they are less popular then they deserve. That's probably because physicists like to think that the best theories they have are not very far from the "final fundamental theory of everything".
 

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To probe small spatial distances, one needs large 3-momenta. But if Lorentz invariance is emergent at large distances and not fundamental at small distances, then large 3-momentum does not necessarily need to correspond to a large energy. For instance, if the dispersion relation is something like
$$\omega^2=c_0+c_2{\bf k}^2+c_4{\bf k}^4+...$$
with ##c_0=m^2\geq 0##, ##c_2=1## and ##c_4<0##, then one can have small energy ##\omega## for a sufficiently large momentum ##|{\bf k}|##.
But is it not de Broglie wavelength of a particle is not related to Lorentz invariance? So if Lorentz invariance not valid at small distances, how could it remove the need for de Broglie wavelength?

Using your 3-momentum details. Does this mean one can probe the planck scale using low energy fundamental particles (if there was such a thing, of course)?
 

Demystifier

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But is it not de Broglie wavelength of a particle is not related to Lorentz invariance?
It is not, de Broglie wavelength formula is true even in nonrelativistic QM.

Using your 3-momentum details. Does this mean one can probe the planck scale using low energy fundamental particles (if there was such a thing, of course)?
If by Planck scale you mean Planck distance (not Planck time), then yes.
 
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It is not, de Broglie wavelength formula is true even in nonrelativistic QM.
Right now, we can't probe the planck scale (or even above certain TeV) because of insufficient energy (the de Broglie wavelength not small enough). So if Lorentz invariance was not fundamental at small scale. Won't large de Broglie wavelength still prevent probing the small scale?

If by Planck scale you mean Planck distance (not Planck time), then yes.
Yes planck distance. Could the fundamental particles in your paper be planck size? So it doesn't require high energy at all?
 
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I need to get to the bottom of this (pun unintended). Before or the same time I ask Demystifier for more details. I'd like some elaboration of the input of Nugatory:

I said: if Lorentz invariance is emergent at large distances and not fundamental at small distances....”
Nugatory: "The word “if” is important here. If Lorentz invariance does not apply at sufficiently small scales then the relationship between energy and three-momentum (the more of one, the more of the other) that we know and love might break down."

Reference https://www.physicsforums.com/threads/why-3-momenta-lorentz-invariance-large-energy.974332/#post-6202402


Nugatory. What is the connection of Lorentz invariance to sufficiently small scales such that without it,
the relationship between energy and three-momentum (the more of one, the more of the other) that we know and love might break down?

Remember as Peterdonis mentioned in the other thread that


peterform1.JPG


Reference: https://www.physicsforums.com/threads/why-3-momenta-lorentz-invariance-large-energy.974332/#post-6202402

" Is this only for large scale? What does sufficiently small scale mean?

Demystifer. Please give more details also so experts and non-experts alike would be more familiar with your formulas and details.

Unfortunately they are less popular then they deserve. That's probably because physicists like to think that the best theories they have are not very far from the "final fundamental theory of everything".
But remember Witten is one proponent of condense matter concept (see his paper in the OP). Since he is a great leader in physics. Then we should at least explore what he mentioned or ramifications..
 
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To probe small spatial distances, one needs large 3-momenta. But if Lorentz invariance is emergent at large distances and not fundamental at small distances, then large 3-momentum does not necessarily need to correspond to a large energy. For instance, if the dispersion relation is something like
$$\omega^2=c_0+c_2{\bf k}^2+c_4{\bf k}^4+...$$
with ##c_0=m^2\geq 0##, ##c_2=1## and ##c_4<0##, then one can have small energy ##\omega## for a sufficiently large momentum ##|{\bf k}|##.
Demystifier. Let me focus on the above directly.
In Newtonian mechanics, large 3-momentum still does correspond to large energy. It is not enough just for Lorentz invariance to no longer hold as Peterdonis put it in https://www.physicsforums.com/threads/why-3-momenta-lorentz-invariance-large-energy.974332/ . This is because:

peterform1.JPG


For the relativistic case.
What are the normal values of c0, c2, c4. where does for example the term
ck2.JPG

come from?

Even experts were stumped. So kindly elaborate and give some references about how Lorentz invariance is related to sufficiently small scales where in such case the relationship between energy and three-momentum (the more of one, the more of the other) that we know and love might break down if there is no Lorentz invariance? how does this relate to the following equations?

peterform1.JPG
 

Demystifier

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In the normal relativistic case, ##c_0=m^2##, ##c_2=1##, ##c_4=0##, I thought it was obvious.
 
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In the normal relativistic case, ##c_0=m^2##, ##c_2=1##, ##c_4=0##, I thought it was obvious.
But the dispersion relation for non-relativistic one is E=p^2/2m. So still large p means large E. How is this nullified in your case using the same E=p^2/2m?
 

Demystifier

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But the dispersion relation for non-relativistic one is E=p^2/2m. So still large p means large E. How is this nullified in your case using the same E=p^2/2m?
E=p^2/2m is the free non-relativistic dispersion relation. For a non-free case, non-relativistic dispersion can be different.
 
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E=p^2/2m is the free non-relativistic dispersion relation. For a non-free case, non-relativistic dispersion can be different.
Any reference to distinguish between free and non-free case?

Btw.. what is the following dispersion relation formula exactly called (where did you get it)? How come even an expert relativist like Peterdonis doesn't considered it part of normal equation for dispersion relation for either relativistic or non-relativistic case?
Kindly elaborate for the experts too because they are stumped or doubt it could work.

"For instance, if the dispersion relation is something like
$$\omega^2=c_0+c_2{\bf k}^2+c_4{\bf k}^4+...$$
with ##c_0=m^2\geq 0##, ##c_2=1## and ##c_4<0##, then one can have small energy ##\omega## for a sufficiently large momentum ##|{\bf k}|##."
 

Demystifier

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How come even an expert relativist like Peterdonis doesn't considered it part of normal equation for dispersion relation for either relativistic or non-relativistic case?
I think you misunderstood him. He only objected that the idea that the relativistic Standard Model of elementary particles emerges from a non-relativistic theory is not an established fact.
 
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Just by assuming that ##\omega^2## is an analytic function of ##{\bf k}^2## you get an expansion of the form I outlined. Literature on condensed matter physics is full of such dispersion relations. For an example see https://en.wikipedia.org/wiki/Phonon#Dispersion_relation
Ok. I will review condense matter physics because it is quite elegant.

About non-relativistic QM being more fundamental than relativistic QFT (which is only an approximation) . I guess this is called Proto QM (Holger Bech Nielsen's). Did Witten also subscribe to this? So far. Only Nielson and you subscribed to it? How about Volovik?
 

Demystifier

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Did Witten also subscribe to this? So far. Only Nielson and you subscribed to it? How about Volovik?
Witten and Volovik perhaps did not claim that explicitly, but to some extent it seems to be implicit in their work.
 
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Witten and Volovik perhaps did not claim that explicitly, but to some extent it seems to be implicit in their work.
So far up to what scale have experimental constrains show the normal momentum and energy still hold? perhaps if there were subquarks, these can be described with low energy fundamental particles?

How about strings. What would string theory look like if they don't have very high energy in that planck scale?
 

Demystifier

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So far up to what scale have experimental constrains show the normal momentum and energy still hold?
It's defined by the LHC scale.

How about strings. What would string theory look like if they don't have very high energy in that planck scale?
String theory is Lorentz invariant by assumption.
 
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It's defined by the LHC scale.
So how can one in principle test it. Using exotic high momentum particle without much energy content to probe the planck scale. Or did you mean the planck scale has high momentum but not much energy (if the idea was correct)?

String theory is Lorentz invariant by assumption.
 

Demystifier

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So how can one in principle test it. Using exotic high momentum particle without much energy content to probe the planck scale. Or did you mean the planck scale has high momentum but not much energy (if the idea was correct)?
The accelerator accelerates a massive particle, which means that it increases its 3-momentum. If Lorentz invariance is violated at sufficiently high momenta, further acceleration of the particle by an accelerator stronger than LHC might result in a decrease of its energy, which would have observable consequences. But despite the small energy one still needs a very strong accelerator for that so it's not something easy to achieve.

Another issue. Such a strong accelerator would still spend a lot of energy, so if the accelerated particle would have little energy, where would the rest of energy go? The particle energy is its kinetic energy (that depends only on momentum), while te rest of energy would go to its potential energy due to interaction with the environment.
 
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Just by assuming that ω2ω2 is an analytic function of k2k2 you get an expansion of the form I outlined. Literature on condensed matter physics is full of such dispersion relations. For an example see https://en.wikipedia.org/wiki/Phonon#Dispersion_relation
To probe small spatial distances, one needs large 3-momenta. But if Lorentz invariance is emergent at large distances and not fundamental at small distances, then large 3-momentum does not necessarily need to correspond to a large energy. For instance, if the dispersion relation is something like
$$\omega^2=c_0+c_2{\bf k}^2+c_4{\bf k}^4+...$$
with ##c_0=m^2\geq 0##, ##c_2=1## and ##c_4<0##

, then one can have small energy ωω for a sufficiently large momentum |k||k|.​
I have read the phonon dispersion relations above. Just to clarify some points.

1. Your statement concerning

"if Lorentz invariance is emergent at large distances and not fundamental at small distances" and
$$\omega^2=c_0+c_2{\bf k}^2+c_4{\bf k}^4+...$$
with ##c_0=m^2\geq 0##, ##c_2=1## and ##c_4<0##

is only valid if the condense matter mechanism existed, right? Because initially I thought it could be valid even without the condense matter thing. This is important to emphasize.

2. Should the fundamental particles still have any wavelength, or is de Broglie wavelength only valid for quasiparticles? Can the fundamental particles occur without any wavelength?

3. Can HUP be cancelled in the fundamental particles? Because to enclose them in very small space, momentum would be so large. I just read the mass paradox problem in preons where the mass in such confined space would be so large (about
200 GeV/c, 50,000 times larger than the rest mass of an up-quark and 400,000 times larger than the rest mass of an electron).
 

Demystifier

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1. can be true even without the condensed matter framework.

If QM is fundamental (which in my approach I assume it is), then De Broglie wavelength and HUP are fundamental.
 
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1. can be true even without the condensed matter framework.
What are framework besides condensed matter framework where it can be true?
 

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