I Theories and their domains of applicability?

  • Thread starter hyksos
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10
7
Modern physics is comprised of a quartet of theory specializations.
I. Classical Physics + Special Relativity S.R.
II. Quantum Mechanics. QM
III. Quantum Field Theory QFT
IV. General Relativity GR

Under what practical conditions do the predictions of each of these theories become salient? I plan to put together a diagram plot of Temperature against size scales exhibiting the extreme conditions required for the modern theories to start to describe observed phenomena. But I want it to be fit for a textbook, so I want my numbers to be truthful to the discipline of physics.

This figure is not a claim on my part. It is likely very wrong right now. That's fine. This is just a back-of-napkin drawing I threw together in a few minutes.

DomainsOFphysics.png

The final diagram should exhibit the following attributes to the viewer :
1 "Quantum Gravity" will be a razor-thin section along the bottom and righthand side of diagram, likely with an arrow pointing at a tiny gap. This should show the extremes required before that theory is needed to make practical predictions.
2. The section CLASSICAL PHYSICS will take up the vast majority of the diagram's space on the page. This should jump out at the reader. The vast majority of phenomenon in our daily lives is adequately described by classical physics.
3. Astronomical temperatures are required before the effects of QFT become "salient" to the unfolding physics. But also very tiny size scales. There is some confusion on the lefthand side here regarding temperatures. I hope we can hash this out in comments.

Notice there is a slight rise in the QM section approaching zero kelvin. Some recent lab experiments have put aluminum nitride cantilevers into a superposition, and the popular articles headlined this as "Macro-scale drumhead placed into superposition". This is a problem regarding at which size scale do the effects of QM "cut off"? Or do they cut off? As far as we know, the cantilevers were placed under high vacuum and cooled to something like 10^-7 Kelvin. But I am willing to make some changes there if someone really pushes back.

Your thoughts?
 

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I. Classical Physics + Special Relativity S.R.
II. Quantum Mechanics. QM
III. Quantum Field Theory QFT
IV. General Relativity GR
I would either split classical and SR or merge QM and QFT. It doesn’t make sense to categorize them this way
 
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I think the CM SR split is a better approach since CM works well with slow speeds and SR with high speeds. Similar analogies can be made for QM and QFT.

From Physics Stackexchange, they talk about the differences of QM and QFT that would be relevant to your map.


Lastly, the Domain of Science channel on Youtube has a map of Physics not unlike what you are trying to develop but with a finer breakdown:

 
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Thanks for the video. However, it is not quantitative enough for what I'm looking for. I know the boundaries are fuzzy between these things, and this is not as clean as a phase transition diagram, but I'm looking for pointed answers to these questions :

1.
At ~ 290 K , at what size scale do the effects of Quantum Mechanics begin to dominate physical interactions?

2.
At 10^-9 K at what size scale do the effects of QM begin to dominate the physics?

3.
Say we are considering size scales of around one centimeter. At what very high temperature would you be forced to use QFT to predict anything about the physics?


1. (I believe the answer is sub-molecular scales. Correct me if I'm wrong.)
2. (Does QM have a cut-off scale?? It seems we could pin this to recent experiments, i.e. cantilevers in superposition, without philosophical speculation.)
3. ( I think the answer is 10^12 Kelvin. Correct this statement if wrong.)
 
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I would either split classical and SR or merge QM and QFT. It doesn’t make sense to categorize them this way
Dale,

I have some questions regarding this distinction between QM and QFT.

I am going to make some statements to the best of my understanding, and feel free correct any of these statements as you see fit.

From the perspective of around submolecular scales 10^-9 meters. Let me define an interval here. [10^-11 m , 10^-9 m] There is a temperature range where QM has to yield to QFT. Some percentage of the particles involved will be moving at relativistic speeds, and may even undergo decay events. I believe this temperature is 10^12 Kelvin. I'd love to hear any disagreements you have.

Even at cooler temperatures, there is a size scale under which QM must yield to QFT, because the vacuum interactions become salient. QM does not have any description of these interactions with "virtual particles", but QFT does. (As a random guess just thrown off the top of my head) this size scale is something near 10^-19 meters.

Your thoughts?
 

f95toli

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1.
At ~ 290 K , at what size scale do the effects of Quantum Mechanics begin to dominate physical interactions?

2.
At 10^-9 K at what size scale do the effects of QM begin to dominate the physics?
There is no answer to these questions; it will be completely determined by what you are looking for and the relevant energy scales for that particular system. There is simply no general answer; not even a "fuzzy" one.
 

Paul Colby

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So, I would put a dot on or close to the intersection of QFT and QM and label it "Your cell phone is here"
 
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Your cell phone is classical. It is designed, understood, and used classically.
 

f95toli

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Your cell phone is classical. It is designed, understood, and used classically.
I disagree. I understand where you are coming from and it is true for the RF bit; but semiconductors can only be understood using QM.
In moderns microfabricated circuits you even need to take tunneling into account since it affects the performance of the transistors (e.g. leakage currents). I would also argue that say the OLEDs that are used to make the screen are "QM" in nature.
 

Paul Colby

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Your cell phone is classical. It is designed, understood, and used classically.
Cool, I was unaware there was a classical theory for any semiconductor devices. Also, aren't both relativities used in GPS? My comment was made only partly in jest. Modern physics very much plays a role at nearly every level of our technology.
 
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semiconductors can only be understood using QM
By that standard everything is QM since atoms can only be understood using QM.

All of a transistor’s use in circuit design is based on the classical voltage/current curves. You need QM to derive the V/I curves, but classically you can just treat them as a constitutive relationship as you do with any material properties.
 

kith

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In order to get a heuristic diagram which allows us to separate the different fundamental regimes of physics, the most sensible thing to start with is a chart of speed vs. action. These can be measured as fractions and multiples of [itex]c[/itex] and [itex]\hbar[/itex] which set the fundamental scales for special relativity and quantum mechanics. This gives us four regimes: quantum mechanics (small speed, small action), classical mechanics (small speed, big action), special relativity (big speed, big action) and quantum field theory (big speed, small action).

We could try to add another dimension to the diagram which determines when general relativity is relevant and when not, but I'm not sure how to do this and whether all of the 8 resulting regimes will be physically meaningful. If we use mass as the third dimension, the mass scale could be determined by the Planck mass (which is determined by [itex]G[/itex] in addition to [itex]c[/itex] and [itex]\hbar[/itex]). But this mass alone doesn't determine when general relativity needs to be used because it is quite small compared to the masses of everyday life.

If you want to include temperature, you could continue this process by introducing an additional dimension of temperature where the Planck temperature sets the scale (which is determined by [itex]k_B, c, \hbar[/itex] and [itex]G[/itex]). But this can't be visualized in 3-D anymore.

To sum up: I think that the first step of this precedure is pretty meaningful. I don't think that your inital goal -distinguishing all regimes of fundamental physics in a diagram of length vs. temperature- can be accomplished in a meaningful way because a) it's questionable whether these two dimensions are good to separate fundamental regimes and b) fundamental physics varies along more than two dimensions. The right way to incorporate other regimes would be to introduce more dimensions in the speed vs. action diagram but I think the value of this is quite limited.

In any case, this is a heuristic. The distinctions between the regimes are necessarily fuzzy and depend on considerations by humans (e.g. relativistic corrections for GPS positions are needed in order to make them accurate enough for our needs).
 
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f95toli

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By that standard everything is QM since atoms can only be understood using QM.
It is not the same thing. Someone working on circuit design at the level of individual "cells" of modern ICs will need to have at least some knowledge about QM simply because it does affect the design (e.g. the aforementioned leakage current). The same is very much true for anyone working with III-V components such as GaAs or GaN heterostructures (LEDs etc) where a lot of the the design is done using quantum wells.

Hence, the design process for a phone will almost certainly involve people with a knowledge of QM. The same would not be true for e.g. a typical bridge.
 
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Someone working on circuit design at the level of individual "cells" of modern ICs will need to have at least some knowledge about QM simply because it does affect the design (e.g. the aforementioned leakage current).
I am fairly skeptical about this. This is not my area of expertise, but as far as I know IC design treats quantum effects simply as constitutive corrections to classical circuit design. Ie they add leakage currents classically as standard circuit design components using measured current voltage relationships rather than calculating what the current voltage relationship should be using Schrodinger’s equation. Do you have a reference that supports that IC design is actually done using Schrodinger’s equation or similar truly quantum calculations?

The same is very much true for anyone working with III-V components such as GaAs or GaN heterostructures (LEDs etc) where a lot of the the design is done using quantum wells
Sure, no dispute there.
 

f95toli

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I am fairly skeptical about this. This is not my area of expertise, but as far as I know IC design treats quantum effects simply as constitutive corrections to classical circuit design. Ie they add leakage currents classically as standard circuit design components using measured current voltage relationships rather than calculating what the current voltage relationship should be using Schrodinger’s equation.
I don't think you need to solve SE to "use" QM. The people doing the design at the cell level (which is the "hardware bit", not the same thing as IC design using e.g. VHDL) should certainly know how to do this, but I agree that it is unlikely that it is done during "normal" design.

However, the same is true for many areas. I haven't solved an SE in years and I work on HW for quantum computing(!). I simply don't have to because most of the work I do these days is done at the circuit level. I would still argue that I am "using QM" in my work.
 

Paul Colby

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I think the key issue is QM was very prominent in the invention and subsequent development of semiconductor devices. Sure, circuit designers don't solve the Schrodinger equation as part of design, but the diode equation follows from QM.
 
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I don't think you need to solve SE to "use" QM.
I guess that is the source of the disagreement then. That is where I tend to draw the dividing line. But at that point it is a classification distinction, not a substantive one.

I work on HW for quantum computing(!)
Hmm, I should probably just defer to you on this then.
 

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