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# Does a gravitating body have to undergo gravitational collapse?

1. Aug 30, 2011

### zonde

Imagine body that has mass and volume such that it is just a bit short of turning into the black hole. Now let's say that the body has been around for some time and has reached present state in some smooth process so that it can be in equilibrium state if such an equilibrium exists.
I assume that this equilibrium state is such that density of mass increases proportionally with the radius so that event horizon does not form anywhere inside the body. Now as the pressure increases so does temperature. Now if the heat will escape from inside of the body toward outside then inside will collapse.
But can it really escape? Photons going in outward direction are redshifted but photons going inward are blueshifted. So it seems that inside of the body can not really cool down.
Of course photons will escape from surface of the body but then there are photons coming from the rest of the universe that would be highly blushifted.

So does this reasoning seems valid? Can a static body exist without undergoing gravitational collapse even without considering degeneracy pressure?

2. Aug 30, 2011

### Staff: Mentor

This is a non-trivial constraint. I believe there is a lower limit to the radius of such a static equilibrium state; I think it's 9/8 of the Schwarzschild radius. I'll see if I can find an online reference (I believe the limit was first derived in a paper by Einstein some time in the 1930's). So any object with a radius less than that *must* collapse to a black hole; it can't exist in a static equilibrium state at all.

It's worth expanding a little bit on how this happens. Heat escaping from the body means the body itself is losing energy; losing energy means it has to contract, i.e., its radius has to decrease. (This is assuming that there is no other source of energy inside the body, for example, it can't undergo nuclear reactions as a star does.) Eventually, its radius will decrease enough that it is smaller than the limit I referred to above, and at that point, it will collapse.

(Of course this is not the *only* way an object could collapse to a black hole. But we're not talking about something like a supernova explosion; we're talking about a slow, "smooth" process, as you put it, where everything changes very gradually.)

No, this is not correct. The blueshift/redshift is really a red herring; in order to measure the net energy loss of the body, you have to pick a single radius at which to do it. Normally this is done "at infinity", i.e., at a very, very large radius, far away from the body, where spacetime is very, very close to flat. At that large radius, you balance outgoing radiation against incoming radiation, and the blueshift/redshift doesn't enter into it. If (as is highly likely with a radiating body in our universe), there is more outgoing radiation than incoming radiation, then the body is losing energy.

You could also, of course, do the energy balance at a much smaller radius, say just outside the surface of the body. There, the incoming radiation would indeed be blueshifted, but the outgoing radiation would *not* be redshifted (because it hasn't yet "climbed out" of the body's gravity well). So the balance would still work out the same. (Basically, since you have to do the comparison at a constant radius, changing the radius changes both the outgoing and incoming radiation in concert, so the balance between them doesn't change.)

Bottom line, under the conditions as described above, no; it would continually lose energy by radiation until its radius was below the limit I described above, and then it would collapse.

Of course, any real object under such conditions would be subject to degeneracy pressure, since that will occur whenever you squeeze matter to a high enough density. So an object like a white dwarf or a neutron star can indeed exist indefinitely in a stable equilibrium after it has radiated away all the energy it can (provided its radius is larger than the limit I gave above--that limit applies even in the presence of degeneracy pressure).

3. Aug 31, 2011

### zonde

Well, yes balance between incoming and outgoing radiation doesn't change with radius.
But I still think that blueshift/redshift is relevant.

Let's look at such a setup. We have two bodies held at different heights above the surface of planet. Bodies are emitting only black body radiation. They emit this radiation only toward each other as they are surrounded by ideal mirrors from other sides.

Let me illustrate this schematically
Code (Text):

b1
|            |
|<R<<<<<<<<B<|
|            |         (planet)
|>R>>>>>>>>B>|
|            |
b2

"b1" and "b2" are two surfaces of bodies emitting black body radiation and ">R>" and ">B>" are redshifted or blueshifted photons of black body radiation.

As you can see net balance across two interfaces for incoming and outgoing radiation is zero and yet two bodies will have different temperature after reaching equilibrium.

4. Aug 31, 2011

### Staff: Mentor

This is true in the idealized situation you've described, but it's not relevant to your original question because you've changed the situation. Your original question was whether a gravitating body in static equilibrium could lose energy by radiation. There were no ideally reflecting mirrors involved; obviously the presence of ideally reflecting mirrors changes the physics of the situation. In the presence of ideally reflecting mirrors as you describe, obviously the body cannot lose any net energy to the universe outside the upper mirror.

The key to whether the body can lose energy, in the original scenario, is that, as you appear to agree, the net energy balance across a surface at a given radius is independent of the radius. The actual equilibrium temperature, given the net energy balance, may be dependent on radius, but what matters for whether the body can lose energy by radiation is the net energy balance, not the equilibrium temperature. As long as the net energy balance is negative (the body radiates away more energy than it takes in, as evaluated across a surface at a given radius), the body will lose energy.

5. Sep 3, 2011

### zonde

I think that I am more interested about temperature gradient that does not contribute to conduction. There is some ground level temperature of universe so if we have this gradient steep enough energy loss can go to zero even with high temperature at the middle of gravitating body.

And after a bit of thinking it seems to me that this question is more about classical physics.
If we model temperature as motion of particles then this motion slows down as we go against gravity and speeds up as we go along. Basically if we don't have convection in material (it's solid) then equilibrium temperature gradient implied by this classical model can be much more steeper than from gravitational redshift.

6. Sep 3, 2011

### Staff: Mentor

Do you really mean just "conduction" or do you mean "heat transfer" in general? Conduction is only possible through a material, not through vacuum, so you can easily have two objects at widely different temperatures separated by vacuum that can't exchange heat through conduction (or convection, for that matter). But they can still do so through radiation. If you are trying to say there can be a temperature gradient that does not contribute to heat transfer in any form, I'm not sure that's possible. Any object at a non-zero temperature radiates.

If this is just another way of describing the conversion between kinetic energy and gravitational potential energy of a given particle, then OK. But that in no way rules out heat transfer between particles.

No, you would still have conduction (and radiation; individual atoms in the solid can still exchange radiation with each other).

7. Sep 4, 2011

### zonde

Hmm, I thought that my example clearly demonstrated that this is possible.
Heat transfer is difference between incoming and outgoing radiation. If outer layer of gravitating object is at temperature around 2.7K it will be in equilibrium with CMB radiation. So as we go closer to the center of gravitating object and redshift/blueshift increases we will have increase in temperature that can not be radiated away.

So basically you are saying that temperature and conduction can not be modeled as motion of individual particles, right?

8. Sep 4, 2011

### Staff: Mentor

Your example shows this *only* if the rate of temperature increase is *exactly* the same as the rate of gravitational blueshift. But in your example, that is only true because the two mirrors are separated by vacuum, and only exchange heat by means of radiation that blueshifts/redshifts with radius at exactly the "gravitational" rate. Your example does not account for heat transfer *within* the gravitating body inside the inner mirror (we'll assume that the outer mirror is exactly at the CMBR temperature so it is in equilibrium with the rest of the universe). Inside the gravitating body, there is not a vacuum, there is matter present; and in the presence of matter (a) the rate of "gravitational blueshift" is different than in vacuum, and (b) the rate of temperature increase as you move inward is governed by factors other than gravity; in the simplest case, the matter is a perfect fluid and is in hydrostatic equilibrium. Unless you can show that in the presence of matter, such as a fluid in hydrostatic equilibrium, the temperature rises as you go inward at *exactly* the same rate as the gravitational blueshift, you haven't supported your case. See next comment.

I'm not saying that at all. What I *am* saying is that the motion of the individual particles, in any real substance, is affected by factors other than gravity. Even if we leave out degeneracy pressure, what about ordinary fluid pressure? (Which is due to the fact that when individual particles in the fluid get close enough, they repel each other--in ordinary fluids the repulsion is due to electromagnetic interactions between the electron shells of the fluid atoms/molecules.)

For an actual example, consider the Earth, which behaves fairly close to a perfect fluid (the Earth does have deviations from perfect fluidity because portions of it are solid, but we'll leave out any such complications here, since they only cause an error of a few percent in the calculation). The temperature at Earth's surface is about 300 K; the temperature at the center is about 5,700 K, or about 19 times that at the surface. However, the gravitational blueshift from the surface to the center of the Earth is only about one part in a billion. So temperature rises inside the Earth a *lot* faster than gravitational blueshift does, because hydrostatic equilibrium causes the ordinary pressure to rise very quickly (the pressure at the center is about 3 *million* times that at the surface), which forces the temperature to rise by ordinary thermodynamics.

Reference for temperature and pressure at center of Earth:

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

Thread where formula for time dilation at center of Earth is given (the blueshift is given by the same formula):

So for any non-vacuum substance to behave as you're suggesting, it would have to have no ordinary pressure, not just no degeneracy pressure. But for any real substance to be in a stable equilibrium at a given radius, it *has* to have ordinary pressure; otherwise there would be nothing opposing its gravity and it would just collapse. But in any substance with ordinary pressure included, as we've just seen, temperature rises a *lot* faster than gravitational blueshift.

It is true that the Earth has internal sources of heat (radioactivity) and receives heat from the Sun, which is how it stays in equilibrium at a hotter temperature than the CMBR. But even if we consider a hypothetical Earth in a stable equilibrium with its surface at the CMBR temperature, the temperature inside would still rise a lot faster than the gravitational blueshift, because of hydrostatic equilibrium.

Last edited: Sep 4, 2011
9. Sep 5, 2011

### zonde

Not sure I understand you.
Let's say that temperature gradient from gravitational blueshift/redshift is "1".
And so you are saying that if temperature gradient is exactly 1 then it will not contribute to heat transfer but if temperature gradient is 1+x then heat transfer will be proportional to 1+x rather than x. Seems weird.

Ordinary fluid pressure is momentum density i.e. motion of the individual particles.
When individual particles are so close that they repel each other then this is called degeneracy pressure.
I believe that electromagnetic interactions are what we can call "collisions".

I will try to respond to the rest of your post later.

10. Sep 6, 2011

### Staff: Mentor

No, I'm saying that you can only attribute the temperature gradient to gravitational blueshift if the rate of increase in temperature is exactly the same as the rate of increase in blueshift. But the rate of increase in temperature is much *larger* than the rate of increase in blueshift, at least in the case I described (the Earth). So the temperature gradient must have some other cause.

Not exactly. Ordinary fluid pressure is caused by momentum *transfer* between the individual particles (or between the particles and external objects like the walls of a container of gas). The momentum transfer occurs when particles get close enough to collide. See further comment below.

No, this is not correct. Degeneracy pressure is a quantum phenomenon; it is caused by the Pauli exclusion principle. It has nothing to do with the ordinary electromagnetic repulsion between the individual particles; it happens even if the particles are electrically neutral and have no repulsive force between them, for example, in neutron stars.

Yes, although I would put it the other way around; what we normally call "collisions" between individual fluid particles, which allow them to exchange momentum, are really repulsive electromagnetic interactions between the particles. Those interactions actually happen at some distance, but for many purposes we can idealize them as happening only on "contact" between the particles.

11. Sep 6, 2011

### zonde

Yes, there are other causes for temperature gradient in case of Earth. But the point I was trying to make was about heat transfer that is caused or not caused by particular temperature gradient and not about causes of temperature gradient.

You said:
I considered my example as an argument in support that there can be such "temperature gradient that does not contribute to heat transfer".

How exactly your argument that "fluid pressure is caused by momentum *transfer*" is correcting my argument that "fluid pressure is momentum density"?
Let me rephrase my statement: Ordinary fluid pressure is proportional to momentum density.
Have you any corrections for that statement?

Degeneracy pressure is not caused by Pauli exclusion principle. Degeneracy pressure is explained by Pauli exclusion principle.
And there is no "ordinary electromagnetic repulsion between the individual particles" that would contribute to pressure if we speak about neutral fluid.

Collisions can happen even between electrically neutral particles like neutrons. I am not sure that I am buying your "repulsive electromagnetic interactions" model.

12. Sep 6, 2011

### zonde

I have to say that I changed my mind. It seems that for fluids pressure is not proportional to momentum density. This hold only for ideal gas.

13. Sep 6, 2011

### Staff: Mentor

I understood your argument slightly differently. I understood your argument to be that there can be a temperature gradient *solely due to the difference in gravitational potential* that does not contribute to heat transfer. My point is that that can only be the case if the temperature gradient is the same as the potential gradient. The only example we've discussed so far where that is the case is your example with the two mirrors, and the only reason the gradients are the same there is that the mirrors are separated by vacuum. Inside the inner mirror (i.e., within the substance of the gravitating body whose surface is the inner mirror), the temperature gradient will *not* be the same as the gravitational potential gradient.

I know you changed your mind about saying that fluid pressure *is* momentum density, but let me clarify the point I was making here anyway. My point is that fluid pressure requires momentum *exchange* between particles; just momentum density by itself isn't enough.

I'm not sure I see the distinction you are trying to make here. Maybe I wasn't clear enough about what I meant. When I said degeneracy pressure is "caused" by the Pauli exclusion principle, I meant that it is a quantum phenomenon that happens because the particles in question are fermions, so no two of them can be in the same state. When a fluid composed of such particles is compressed, it resists the compression because the more compressed it is, the more the wave functions of the individual particles overlap, meaning they are closer to being in the same state.

Ordinary fluid pressure, by contrast, is a classical phenomenon; it does not depend on any quantum properties of the individual fluid particles. A fluid composed of bosons still exhibits ordinary fluid pressure, even though bosons are not subject to the Pauli exclusion principle and there is nothing prohibiting every boson in the fluid from being in the same quantum state.

This is true, and I did not phrase this part of what I was saying very well. The key point is that "collisions" can happen between the fluid particles. See next comment.

You are correct that "collisions" between fluid particles do not *have* to be caused by electromagnetic repulsion. But they *can* be. In an ordinary fluid composed of atoms or molecules, the collisions are due to electromagnetic repulsion between the electrons in the outer shells of the atoms or molecules. And yes, this happens even though the atoms or molecules, as a whole, are electrically neutral. That is all I meant by my "repulsive ectromagnetic interactions model". Do you dispute that this happens in an ordinary fluid composed of atoms or molecules? If so, how do you think the collisions happen in such a fluid?

In a fluid composed of neutrons, such as the interior of a neutron star, you are correct that there are no "collisions" due to electromagnetic repulsion. However, neutrons still interact by means of the strong nuclear force, so they can still exchange momentum by "collisions" mediated by that force. The strong nuclear force is attractive at ranges comparable to the size of an atomic nucleus, so the interactions between neutrons at that range are not what we normally think of as "collisions". However, it is believed that the strong force becomes repulsive at shorter ranges, and "collisions" between neutrons mediated by this repulsion are believed to produce a measurable ordinary fluid pressure in neutron stars (although the majority of the observed pressure is still due to degeneracy pressure).

Last edited: Sep 6, 2011
14. Sep 6, 2011

### Staff: Mentor

Can you give an explicit demonstration of this? I can't get this from either form of the ideal gas law that I'm familiar with:

$$P = nkT$$

where n is the number density (number of particles per unit volume), k is Boltzmann's constant, and T is temperature; or:

$$P = \rho R T$$

where $\rho$ is the mass density, R is the gas constant per unit mass for the particular substance, and T is temperature. I can't see any way to get from either of these equations to the claim that fluid pressure is proportional to momentum density. I can see the proportionality to *energy* density (which is basically what both equations say), but that's not the same as *momentum* density.

15. Sep 6, 2011

### utesfan100

Might the temperature, roughly an estimate of the average particle energy, not be Lorentzian invariant?

This appears to be a solid argument for temperature measurements being hotter from frames deeper within a gravitational field, with the increase in temperature exactly that needed to balance the blue shifting of the black body radiation.

16. Sep 6, 2011

### Staff: Mentor

Energy by itself isn't Lorentz invariant, so one would not expect temperature to be either. For an individual point particle, the invariant object is the energy-momentum 4-vector. For a continuous substance like a fluid, the invariant object is the stress-energy tensor. In either case, energy (and hence temperature) is only one component of the full object, and so it will be different in different frames.

This is actually a separate question from the above. Asking whether a quantity is "Lorentz invariant" is asking whether its value at a single event in spacetime is the same for observers in different states of motion passing through that event. What you are talking about here is the change in the value of the quantity as you change locations--i.e., the difference in its value at different events. When you do that, you have to be very careful about specifying how you are going to compare observations made at different events.

For example, consider the "mirror" scenario that zonde described earlier in this thread. The temperature at the "lower" mirror, in that scenario, is "blueshifted" from the temperature at the "upper" mirror by exactly the right amount to balance the blueshift in radiation as it goes deeper into the gravitational field. However, that only holds because, as I've noted several times now, the space between the mirrors is vacuum, and the only heat exchange between the mirrors is radiation. Of course radiation traveling in vacuum in a gravitational field is going to blueshift/redshift by exactly the "right" amount to balance the change in gravitational potential; but that in itself does not show anything about what will happen when the intervening space is *not* vacuum, or when other mechanisms of heat transfer are available.

I suppose it might still be useful to compare, for a given situation, the "blueshifted" temperature at some radius with the *actual* temperature measured at that radius. For example, I quoted temperatures for the Earth in an earlier post: a surface temperature of 300 K, and a temperature at the center of about 5700K. One could also defined a "blueshifted" temperature at the center, by taking the 300 K at the surface and multiplying by a "blueshift factor" based on the change in gravitational potential from surface to center. Since that change is about one part in a billion, the "blueshifted" value of the surface temperature, at the center, would be about 300.000000003 K. Obviously this is a lot cooler than the *actual* temperature at the center, which was my point. But you could, I suppose, say that the "actual" change in temperature, "corrected for blueshift", was not 5700/300 (a factor of 19), but 5700/300.000000003 (a factor of a smidgen less than 19).

17. Sep 8, 2011

### zonde

And your idea is that within body after reaching equilibrium (no net transfer of heat) temperature gradient is 0, right?
If that's right what mechanism of heat transfer is responsible for that?

Does photon gas have pressure? Photons can collide with walls of container (mirrors) but there wouldn't be collisions between photons.

There are no boson fluids. The only real boson we can investigate more or less directly is photon and there are no photon fluids that we know of. We can speak only about something like photon gas.

Maybe you mean fluids consisting of "bosonic-composites" like Helium-4? They are still subject to Pauli exclusion principle.

Hmm, there of course is repulsion between particles of fluid. Do we have to agree exactly how we call this repulsion and how this repulsion should be "explained"? What do you say?

18. Sep 8, 2011

### zonde

Not sure that I can give you satisfactory answer.
Well it seems right to me. Pressure is caused by kinetic energy of particles (I am using kinetic theory). If you decrease volume of ideal gas pressure increases in inverse proportion. Density is some physical quantity per volume. So it fits.

19. Sep 9, 2011

### Staff: Mentor

All I've been saying so far is that the temperature gradient will not be the same as the gradient in gravitational blueshift for a non-vacuum body. The question of whether there can still be *any* temperature gradient in a body at equilibrium is more complicated, and I'll discuss it in a separate post after I've thought about it some more.

To first order, you are correct, there are no collisions directly between photons (there are indirect, higher-order photon interactions when quantum vacuum polarization is taken into account). However, a photon gas is a little complicated because you can't really model it as a typical non-relativistic fluid (because photons are by definition relativistic particles). To really model a photon gas, you have to use a relativistic stress-energy tensor, and the only ones I've ever seen for a "photon gas" (such as the one used to describe a radiation-dominated universe) all have nonzero pressure components.

A gas is a fluid. "Fluid" does not just mean liquid.

The individual fermions that are bound together to form the He-4 atom do, yes. But He-4 atoms themselves, as particles in a fluid, don't. If they did, He-4 would not become superfluid at low enough temperatures; a superfluid is a Bose-Einstein condensate.

As long as you agree that there is *some* kind of repulsion between particles in a fluid, I have no problem. I was only objecting because you seemed to be saying that the *only* possible type of repulsion was electromagnetic, or perhaps you thought that's what I was saying. Obviously there are other types of repulsion possible, and it now seems to me that you agree with that.

It's good that the equations I posted seem right to you, since their derivations are a fundamental part of the kinetic theory of gases.

20. Sep 9, 2011

### zonde

Thanks for correction. I somehow associated "fluid" exclusively with liquid.

Oh, I didn't mean equations. As I understood your question it was if using ideal gas equations I can demonstrate that pressure is proportional to momentum density.


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Math Help - Cost

1. The following function represents the cots in hundreds of dollars for producing pens, where x represents 1000's of units
c(x)=.4x^2-16x+200 , 25 ≤ x ≤ 40

a) Estimate the cost for making the 36th 1000-unit run using the marginal cost function derivative.

b) Find the actual cost for making the 36th 1000-unit run.

c) Find the percent margin of error for your cost estimate in part a.

2. Originally Posted by Hallah_az
2. Find the equation of the line tangent to f(x)=1/x at the point x=1
You need to find the derivative.
Thus, you have $f(x)=\frac{1}{x}=x^{-1}$
Its derivative is the power rule, thus,
$f'(x)=(-1)x^{-1-1}=-x^{-2}=-\frac{1}{x^2}$
At, point $x=1$ we have, $y=\frac{1}{1}=1$.
Now we use the point-intercept formula. Which says that if a line passes through point $(x_0,y_0)$ and has slope $m$ then, its equation is,
$y-y_0=m(x-x_0)$. Thus, in this case we have the point, which is $(1,1)$. Now we need the slope. That is the derivative evaluated at that point which is $f'(1)=-\frac{1}{1^2}=-1$ the equation is,
$y-1=-1(x-1)$
Thus,
$y-1=-x+1$
Thus,
$y=-x+2$

3. Thank you!

I got the 2nd part, but I do not understand a) the marginal cost function; b) actual cost; c) the percent margin

format: plain


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# Finding Interger Solutions

Given the following equation:

$$x^3=3^y \cdot 7^z+8$$

Find the integer positive triplet $$(x,y,z)$$ that satisfies the equation.

Enter your answer as $$x+y+z$$

×


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I Relational Hidden Variables (Real ensemble or thermal?)

jlcd

Smolin latest book about the quantum is quite interesting. Its called "Einstein Unfinished Revolution: Search for What Lies Beyond the Quantum" and he has a new theory or interpretation. Id like to know what you make of it. The theory is very simple. Similar views produce QM. May i know how this differs to say Neumaier Thermal Interpretation? You can understand Neumaier's main idea only after reading pages and pages of advanced arxiv papers and i couldnt comprehend its basic thesis the whole year. Is it similar to Smolin's? Can anyone summarize it as i like Smolin ensemble formulation and wonder if Neumaier's is similar to it or how they differ? Smolin book has several hundred paragraphs so its justifed to share the following just so everyone gets the gist or main idea and hence can give feedback if it makes sense and what possible flaws. Thanks.

Now, for big, clunky things like ourselves, made up of vast numbers of atoms, this is as far as it goes. But consider what it takes for atoms to have similar views. Atoms have many fewer degrees of freedom, hence fewer relational properties. So atoms which are far away from each other in space may still have similar neighborhoods, just because there are vastly fewer configurations their local neighborhoods could take. This suggests that perhaps similar atoms, with the same constituents and similar surroundings, interact with each other just because they have similar views.

These interactions would be highly, highly nonlocal. But in my recent work, I have showed that this could be the basis of quantum physics. Consider a hydrogen atom in a water molecule dancing in the air in front of me. This has a first neighborhood consisting of an oxygen atom, and a second neighborhood consisting of the whole molecule. The same is true of every hydrogen atom in a water molecule everywhere in the universe. So I am going to trust my relational instincts and take the crazy step of positing that all these atoms are interacting with each other, just because their views are similar. More specifically, I will posit that the interactions act to increase the differences between these atoms’ views. This will go on until the system has maximized the variety of views the atoms have of the universe.

In a recent paper, I showed that the hypothesis of maximal variety leads to the Schrödinger equation, and hence to quantum mechanics. This happens because there turns out to be a mathematical similarity between the variety and Bohm’s quantum force. As a result, Bohm’s quantum force acts to increase the variety of a system. It does so by making the neighborhoods of all the different particles as different from each other as possible.

In this approach the probabilities in quantum mechanics refer to an ensemble that really exists, the ensemble of all systems with similar views. This is a real ensemble, in that the elements are not located in our imagination; they are, each and every one, a part of the natural world. This is in accord with the principles of causal completeness and reciprocity.

This was the basis of a relational hidden variable theory I proposed, which I called the real ensemble formulation of quantum mechanics. From it, I could derive the Schrödinger formulation of quantum mechanics from a principle that maximizes the variety present in real ensembles of systems with similar views of the universe.

Related Quantum Physics News on Phys.org

A. Neumaier

You can understand Neumaier's main idea only after reading pages and pages of advanced arxiv papers and i couldnt comprehend its basic thesis the whole year.
DarMM gave in post #268 of the main thread on the thermal interpretation a nice summary of it. Post #484 is my very short summary.
Smolin ensemble formulation and wonder if Neumaier's is similar to it or how they differ?
Not similar. The thermal interpretation is deterministic, not an ensemble interpretation. The stochastic features arise as effects of the neglected environment.

jlcd

DarMM gave in post #268 of the main thread on the thermal interpretation a nice summary of it. Post #484 is my very short summary.

Not similar. The thermal interpretation is deterministic, not an ensemble interpretation. The stochastic features arise as effects of the neglected environment.
But that is exactly Smolin theory that the stochastic features arise as effects of the neglected environment! I think you have the same theory, only yours is a Qft completion. I hope you can articulate it to general audience so many can understand. You can't finish one paragraph using using very difficult terms. I think you can write like Smolin so the rest can understand too.

The following is critical Smolin passages and wont quote other paragraphs again. So please bear with me:

"On the technical side, this theory borrows from the many interacting classical universes theory I described in the last chapter, only the ensemble of similar systems does not come from other universes parallel to our own; instead they are similar systems far away in distant regions of our own single universe.

In this theory, the phenomena of quantum physics arise from a continual interplay between the similar systems that make up an ensemble. The partners of an atom in my glass of water are spread through the universe. The indeterminism and uncertainties of quantum physics arise from the fact that we cannot control or observe those different systems. In this picture, an atom is quantum because it has many nearly identical copies of itself, spread through the universe.

An atom with its neighborhood has many copies because it is close to the smallest possible scale. It is simple to describe, as it has few degrees of freedom. In a big universe it will have many near copies.

Large, macroscopic systems such as cats, machines, or ourselves have, by contrast, a vast complexity, which takes a great deal of information to describe. Even in a very big universe, such systems have no close or exact copies. Hence, cats and machines and you and I are not part of any ensemble. We are singletons, with nothing similar enough to interact with through the nonlocal interactions. Hence we do not experience quantum randomness. This is a solution to the measurement problem."

A. Neumaier

Hence, cats and machines and you and I are not part of any ensemble. We are singletons, with nothing similar enough to interact with through the nonlocal interactions. Hence we do not experience quantum randomness. This is a solution to the measurement problem.
The explanation of the ''Hence'' would be a solution to the measurement problem. But an ensemble theory cannot explain any property of singletons - precisely this is the measurement problem! The state of a cat cannot have the interpretation written down in the standard postulates of QM. And given only these foundations, nothing can....

A. Neumaier

Smolin latest book about the quantum is quite interesting. Its called "Einstein Unfinished Revolution: Search for What Lies Beyond the Quantum" and he has a new theory or interpretation.
Lee Smolin said:
In a recent paper, I showed that the hypothesis of maximal variety leads to the Schrödinger equation, and hence to quantum mechanics.
See Quantum mechanics and the principle of maximal variety.

charters

In this theory, the phenomena of quantum physics arise from a continual interplay between the similar systems that make up an ensemble
Similarlty in https://arxiv.org/abs/1104.2822 Smolin says:

"Microscopic systems have indefinite values of beables, while macroscopic systems have definite values, because microscopic systems come in many copies, and so are subject to the copy rule, in which they evolve stochastically by copying the beables of members of the ensemble they share. Macroscopic systems are those that have no copies, anywhere in the universe, hence they are not subject to the copy dynamics."

I think this is trivially inconsistent with QM. We have done interference experiments with large proteins and crystals, and it would be possible to make an experiment where each molecule (of similar mass and size) was internally structurally unique in the experiment., Following QM, we will still expect to see aggregate quantum interference effects over the center of mass measurement, despite Smolin's copy rule not applying. Probably the completed protein interference experiments already had a bunch of this variation due to experimental error.

This whole idea also seems to require a very strict, fundamental particle ontology to even be meaningfully discussed, which is inconsistent with Haag's theorem/interacting QFTs. I cannot see how this distinction of unique/non-unique systems could even get off the ground in a theory fields from which particles are emergent in finite regimes (this being our best concept of physical reality as it stands).

jlcd

Similarlty in https://arxiv.org/abs/1104.2822 Smolin says:

"Microscopic systems have indefinite values of beables, while macroscopic systems have definite values, because microscopic systems come in many copies, and so are subject to the copy rule, in which they evolve stochastically by copying the beables of members of the ensemble they share. Macroscopic systems are those that have no copies, anywhere in the universe, hence they are not subject to the copy dynamics."

I think this is trivially inconsistent with QM. We have done interference experiments with large proteins and crystals, and it would be possible to make an experiment where each molecule (of similar mass and size) was internally structurally unique in the experiment., Following QM, we will still expect to see aggregate quantum interference effects over the center of mass measurement, despite Smolin's copy rule not applying. Probably the completed protein interference experiments already had a bunch of this variation due to experimental error.

This whole idea also seems to require a very strict, fundamental particle ontology to even be meaningfully discussed, which is inconsistent with Haag's theorem/interacting QFTs. I cannot see how this distinction of unique/non-unique systems could even get off the ground in a theory fields from which particles are emergent in finite regimes (this being our best concept of physical reality as it stands).
Wasn't Smolin aware of the experiments with large proteins and crystals or what was his counterarguments?

Are you familiar with Neumaier Thermal Interpretation? Using your own words, can you summarize it using plain english like how Smolin wrote in his book? Neumaier's is the most difficult to understand because his target are all Ph.Ds. So please bring the language down to us at least undergraduates or general book readers. I'm aware of QFT. Was Neumaier arguing that since QM is just effective theory of QFT. The measurement problem vanishes in QFT? But I'm aware it is still the same in QFT. So how does Neumaier solve it? His reasoning seems to be a cat couldn't be described using QM because of fields. Was he arguing there were no particles so measurement problem solved? Kindly briefly give the gist of it in book level approach akin to Smolin book. I like Smolin explanation because there is the elegance to it. I wanna understand Neumaier's basic ideas too to see similarities and differences to Smolin's. So share it using your own words. Imagine you are addressing it to Smolin book readers. Thank you!

charters

Wasn't Smolin aware of the experiments with large proteins and crystals or what was his counterarguments?
I hadn't looked at the 2015 paper above when I commented, but in section 4 there he does mention he thinks that, in an experiment generally along these lines, his theory would predict a departure from regular QM. But he doesn't mention what he has to say about the existing organic molecule experiments, and I think these (or small variations of them) already show the ship has sailed on his proposal. But I haven't read his book or all his papers, so I don't know if he tackles this directly somewhere else.

Are you familiar with Neumaier Thermal Interpretation? Using your own words, can you summarize it using plain english like how Smolin wrote in his book? Neumaier's is the most difficult to understand because his target are all Ph.Ds. So please bring the language down to us at least undergraduates or general book readers. I'm aware of QFT. Was Neumaier arguing that since QM is just effective theory of QFT. The measurement problem vanishes in QFT? But I'm aware it is still the same in QFT. So how does Neumaier solve it? His reasoning seems to be a cat couldn't be described using QM because of fields. Was he arguing there were no particles so measurement problem solved? Kindly briefly give the gist of it in book level approach akin to Smolin book. I like Smolin explanation because there is the elegance to it. I wanna understand Neumaier's basic ideas too to see similarities and differences to Smolin's. So share it using your own words. Imagine you are addressing it to Smolin book readers. Thank you!
I don't really agree that the standard for an interpretation of QM is that it can be described at a popsci level or understandable at a popsci level. My experience is that popsci readers never really understand any interpretation accurately - this goes for Copenhagen, many worlds, Bohm, etc. - and always have a lingering confusion or believe something impossible. I actually think its malpractice for a popsci book or blog to argue on behalf or against any interpretation. Books like this should just try to describe pros and cons of each major option, very neutrally. This is extra true for an idea like Smolin's which predicts deviations from standard QM. A general audience reader won't appreciate how big of a claim this is, and how it really requires extraordinary evidence to ever be accepted.

jlcd

Smolin reasoned there were 3 kinds of anti-realists:

2. quantum epistemologists
3. operationalists

There are two kinds of realists.
1. Naive realists
2. Magical realists.

Both answered yes to these two questions:

"First off, does the natural world exist independently of our minds? More precisely, does matter have a stable set of properties in and of itself, without regard to our perceptions and knowledge?

Second, can those properties be comprehended and described by us? Can we understand enough about the laws of nature to explain the history of our universe and predict its future?"

I read the book two times and very familiar with all the arguments. I just want to know updates of Smolin own realist theory. Second. I want to know where Neumaier belonged to. He is a Witten that we can actually talk too and not inaccessible worlds away. I guess Neumaier is a realist? Is there no experiments that can test Neumaier theory? (I know all interpretations have same math but remember different intepretations have extra math that only future experiments can prove).

I hope all can read Smolin book. The following is from the preface and free at amazon. So let it introduce the best QM book on the planet that introduces the measurement problem. It is one of a kind book. I request Neumaier to write like it too.

THERE ARE DIFFERENT KINDS of anti-realists, which leads to different views on quantum mechanics.

Some anti-realists believe that the properties we ascribe to atoms and elementary particles are not inherent in those objects, but are created only by our interactions with them, and exist only at the time when we measure them. We can call these radical anti-realists. The most influential of these was Niels Bohr. He was the first to apply quantum theory to the atom, after which he became the leader and mentor to the next generation of quantum revolutionaries. His radical anti-realism colored much of how quantum theory came to be understood.

Another group of anti-realists believes that science, as a whole, does not deal in or talk about what is real in nature, but rather only ever talks about our knowledge of the world. In their view, the properties physics ascribes to an atom are not about that atom; they are instead only about the knowledge we have of the atom. These scientists can be called quantum epistemologists.

And then there are the operationalists, a group of anti-realists who are agnostic about whether there is a fundamental reality independent of us or not. Quantum mechanics, they argue, is not in any case about reality; it is rather a set of procedures for interrogating atoms. It is not about the atoms themselves; it is about what happens when atoms come into contact with the big devices we use to measure them. Heisenberg, the best of Bohr’s protégés, who invented the equations of quantum mechanics, was, at least partly, an operationalist.

In contrast to the disputes between radical anti-realists, quantum epistemologists, and operationalists, all realists share a similar perspective—we agree about the answer to both questions I posed above. But we differ on how we answer a third question: Does the natural world consist mainly of the kinds of objects that we see when we look around ourselves, and the things that constitute them? In other words, is what we see when we look around typical of the universe as a whole?

Those of us who say yes to this question can call ourselves simple or naive realists. I should alert the reader that I use the adjective “naive” to mean strong, fresh, uncomplicated. For me, a view is naive if it is not in need of sophisticated arguments or convoluted justifications. I would argue that a naive realism is, whenever possible, to be preferred.

There are realists who are not naive in this sense. They believe that reality is vastly different from the world we perceive and measure.

An example of such a view is the Many Worlds Interpretation, which teaches that the world we perceive is only one of a vast and ever-growing number of parallel worlds. Its proponents call themselves realists, and they have some claim to that designation by virtue of their answering yes to the first two questions. But, in my opinion, they are realists only in the most technical, academic sense. They may perhaps be called magical realists, for they believe that what is real is far beyond the world we perceive. Magical realism in this sense is almost a form of mysticism, for it implies that the true world is hidden from our perception.

zonde

Gold Member
I think this is trivially inconsistent with QM. We have done interference experiments with large proteins and crystals, and it would be possible to make an experiment where each molecule (of similar mass and size) was internally structurally unique in the experiment., Following QM, we will still expect to see aggregate quantum interference effects over the center of mass measurement, despite Smolin's copy rule not applying. Probably the completed protein interference experiments already had a bunch of this variation due to experimental error.
So, you are saying QM predicts interference for distinguishable systems. Well, this is just plain wrong.

charters

So, you are saying QM predicts interference for distinguishable systems. Well, this is just plain wrong.
No I'm not saying that. The interference at issue is internal to the system, not between the systems. Suppose you have a "universal" closed MZI which can do an interference experiment on any particle, atom, or molecule you want - from an electron to a DNA helix - and suppose it is tuned to constructive (destructive) interference in exit port 1 (2). Now you take any random bucket of particles, atoms, and molecules and send systems through the MZI one by one. You will get 100% clicks at port 1, per QM. Smolin is saying there's no QM, but instead this other theory where at some point the molecules get so complex they just won't interfere *in principle*. So, Smolin predicts some molecules click at port 2, and QM says this never happens.

Problem for Smolin is we've confirmed analogous QM interference effects already for some quite complex molecules.

PeterDonis

Mentor
we've confirmed analogous QM interference effects already for some quite complex molecules
Yes, using diffraction gratings, as for example in this experiment with buckyballs:

Note, however, that diffraction gratings are not the same as beam splitters. AFAIK we have nothing analogous to beam splitters, which are essential components of an MZI, for anything other than photons.

Another interesting observation is in section III.B of the above linked paper, which discusses coherence and which path information. The paper notes that the buckyballs can emit radiation during the experiment (because, unlike simpler particles, they have a rich array of excited states and are highly unlikely to be in the ground state when prepared), but that the radiation is weak enough that it does interact significantly with the environment and so does not constitute which path information. But as the objects in such an experiment get more and more complex, it would be more and more likely that enough radiation would be emitted to interact significantly with the environment and therefore provide which path information, destroying the interference.

A mechanism like this could lead to large enough objects not showing quantum interference effects no matter how hard we try, even though this is not "in principle" (you could still theoretically control the preparation process enough to ensure that the objects were all in the ground state and could not emit radiation, but it's not possible in practice). So even if Smolin's empirical claim turned out to be true for large enough molecules (no observed interference no matter how hard we try), it might not establish that his underlying theoretical claim (QM is incomplete) is correct.

charters

Note, however, that diffraction gratings are not the same as beam splitters. AFAIK we have nothing analogous to beam splitters, which are essential components of an MZI, for anything other than photons.
Yes of course - I was just abstracting for (I hoped) clarity. Its the same premise with diffraction.

A mechanism like this could lead to large enough objects not showing quantum interference effects no matter how hard we try, even though this is not "in principle" (you could still theoretically control the preparation process enough to ensure that the objects were all in the ground state and could not emit radiation, but it's not possible in practice). So even if Smolin's empirical claim turned out to be true for large enough molecules (no observed interference no matter how hard we try), it might not establish that his underlying theoretical claim (QM is incomplete) is correct.
Right, this is important. As you say, at a certain point, QM also predicts interference experiments will fail, but in QM this is due to unavoidable decoherence effects. This means the classical limit only seems like evidence for Smolin's proposal because he misattributes the effect to uniqueness/complexity, when really it is just that larger systems decohere more easily, and also can obviously be more complex. It's like the mistake of saying ice cream causes drowning deaths when really people just separately both get ice cream and go swimming on hot days.

The other problem for Smolin is we actually have pretty good control over decoherence for some pretty intricate molecules, which produces a testable regime where Smolin and QM explicitly will disagree. For the record, the real experiment I am thinking off is: https://www.nature.com/articles/ncomms1263

"Our experiments prove the quantum wave nature and delocalization of compounds composed of up to 430 atoms, with a maximal size of up to 60 Å, masses up to m=6,910 AMU and de Broglie wavelengths down to λdB=h/mv≃1 pm. We show that even complex systems, with more than 1,000 internal degrees of freedom, can be prepared in quantum states that are sufficiently well isolated from their environment to avoid decoherence and to show almost perfect coherence."

The proposal here goes even further: https://iopscience.iop.org/article/10.1088/0031-8949/91/6/063007. And there has even been talk of interference with full viruses. Frankly, I'd be shocked if these interference experiments failed, when decoherence is under control.

jlcd

Yes of course - I was just abstracting for (I hoped) clarity. Its the same premise with diffraction.

Right, this is important. As you say, at a certain point, QM also predicts interference experiments will fail, but in QM this is due to unavoidable decoherence effects. This means the classical limit only seems like evidence for Smolin's proposal because he misattributes the effect to uniqueness/complexity, when really it is just that larger systems decohere more easily, and also can obviously be more complex. It's like the mistake of saying ice cream causes drowning deaths when really people just separately both get ice cream and go swimming on hot days.

The other problem for Smolin is we actually have pretty good control over decoherence for some pretty intricate molecules, which produces a testable regime where Smolin and QM explicitly will disagree. For the record, the real experiment I am thinking off is: https://www.nature.com/articles/ncomms1263

"Our experiments prove the quantum wave nature and delocalization of compounds composed of up to 430 atoms, with a maximal size of up to 60 Å, masses up to m=6,910 AMU and de Broglie wavelengths down to λdB=h/mv≃1 pm. We show that even complex systems, with more than 1,000 internal degrees of freedom, can be prepared in quantum states that are sufficiently well isolated from their environment to avoid decoherence and to show almost perfect coherence."

The proposal here goes even further: https://iopscience.iop.org/article/10.1088/0031-8949/91/6/063007. And there has even been talk of interference with full viruses. Frankly, I'd be shocked if these interference experiments failed, when decoherence is under control.
Smolin mentioned quantum computer can test his theory, not protein or buckyball. Does anyone know how to implement it? Smolin interpretation is so superior because its background independent unlike rest of interpretations which have fixed background.

Smolin briefly described quantum computer. But how can two quantum computers interfere?

"I argued that large complex systems have no copies, and hence are not subject to quantum randomness. But can we produce microscopic systems, made from a small number of atoms, which also have no copies anywhere in the universe? Such systems would not obey quantum mechanics, in spite of being microscopic.

We have the capability to do just that using the tools of quantum information theory. Indeed, a sufficiently large quantum computer should be able to produce states involving enough entangled qubits that they are very unlikely to have any natural copies anywhere in the observable universe. This suggests that the real ensemble theory can be falsified by making a large quantum computer that works exactly as predicted by quantum mechanics."

zonde

Gold Member
No I'm not saying that. The interference at issue is internal to the system, not between the systems. Suppose you have a "universal" closed MZI which can do an interference experiment on any particle, atom, or molecule you want - from an electron to a DNA helix - and suppose it is tuned to constructive (destructive) interference in exit port 1 (2). Now you take any random bucket of particles, atoms, and molecules and send systems through the MZI one by one. You will get 100% clicks at port 1, per QM. Smolin is saying there's no QM, but instead this other theory where at some point the molecules get so complex they just won't interfere *in principle*. So, Smolin predicts some molecules click at port 2, and QM says this never happens.

Problem for Smolin is we've confirmed analogous QM interference effects already for some quite complex molecules.
Yes, you made a point. Many different particles with (nearly) identical mass and momentum undergoing self interference in the same setup will contribute to the same interference pattern according to QM.

But even so I agree that Smolin's idea is quite problematic, I'm not sure your argument is correct that the experiment you gave falsifies Smolin's idea. Smolin does not say that complex molecules can't show interference, he says that unique molecules can't show interference. And of course molecules in the experiment are not unique. Experimenters needed quite a bunch of these molecules to perform their experiment.

As I understand Smolin explains interference as non-local interaction between identical systems. My problem with this explanation is - how other identical systems "know" about experimental setup?
Say this experiment with interference of helium atoms in MZ type setup with delayed choice manipulation:
Wheeler's delayed-choice gedanken experiment with a single atom
Fine, particles are identical, but there is single atom in each experimental run. Do atoms from other experimental runs "remember" the setup and pass this information to the particle that is now moving through the setup? This does not seem like serious explanation.
I consider physical ensembles an interesting idea, but if several particles have to pass the setup in order for interference to show up then the only viable option IMO would be to consider possibility that other particles leave the information about the path they traveled in environment. But as I understand Smolin's idea is different.

zonde

Gold Member
Smolin mentioned quantum computer can test his theory, not protein or buckyball. Does anyone know how to implement it? Smolin interpretation is so superior because its background independent unlike rest of interpretations which have fixed background.

Smolin briefly described quantum computer. But how can two quantum computers interfere?

"I argued that large complex systems have no copies, and hence are not subject to quantum randomness. But can we produce microscopic systems, made from a small number of atoms, which also have no copies anywhere in the universe? Such systems would not obey quantum mechanics, in spite of being microscopic.

We have the capability to do just that using the tools of quantum information theory. Indeed, a sufficiently large quantum computer should be able to produce states involving enough entangled qubits that they are very unlikely to have any natural copies anywhere in the observable universe. This suggests that the real ensemble theory can be falsified by making a large quantum computer that works exactly as predicted by quantum mechanics."
It is more reasonable to thoroughly test any new idea against existing experimental results rather then developing new experiments. It is much cheaper and faster. You can eliminate a lot of ideas that does not work this way as we have plenty of experimental data.

jlcd

Yes, you made a point. Many different particles with (nearly) identical mass and momentum undergoing self interference in the same setup will contribute to the same interference pattern according to QM.

But even so I agree that Smolin's idea is quite problematic, I'm not sure your argument is correct that the experiment you gave falsifies Smolin's idea. Smolin does not say that complex molecules can't show interference, he says that unique molecules can't show interference. And of course molecules in the experiment are not unique. Experimenters needed quite a bunch of these molecules to perform their experiment.

As I understand Smolin explains interference as non-local interaction between identical systems. My problem with this explanation is - how other identical systems "know" about experimental setup?
Say this experiment with interference of helium atoms in MZ type setup with delayed choice manipulation:
Wheeler's delayed-choice gedanken experiment with a single atom
Fine, particles are identical, but there is single atom in each experimental run. Do atoms from other experimental runs "remember" the setup and pass this information to the particle that is now moving through the setup? This does not seem like serious explanation.
I consider physical ensembles an interesting idea, but if several particles have to pass the setup in order for interference to show up then the only viable option IMO would be to consider possibility that other particles leave the information about the path they traveled in environment. But as I understand Smolin's idea is different.
See this paper by Smolin. Its also mentioned in the book. https://arxiv.org/abs/1205.3707 part of the abstract reads:

"We also propose that laws of quantum evolution arise from a principle of precedence, according to which the outcome of a measurement on a quantum system is selected randomly from the ensemble of outcomes of previous instances of the same measurement on the same quantum system. This implies that dynamical laws for quantum systems can evolve as the universe evolves, because new precedents are generated by the formation of new entangled states."

A. Neumaier

Smolin latest book about the quantum is quite interesting. Its called "Einstein Unfinished Revolution: Search for What Lies Beyond the Quantum" and he has a new theory or interpretation.
Lee Smolin said:
In a recent paper, I showed that the hypothesis of maximal variety leads to the Schrödinger equation, and hence to quantum mechanics.
I now read Smolin's Quantum mechanics and the principle of maximal variety, which contains the technical material. He proposes a theory with an ensemble of $N$ identically structured systems in a $d$-dimensional multiparticle configuration space interacting with each other via a strange, messy multiparticle action (19), which is mathematically ill-defined since the complex logarithm is multivalued.

He shows that in the limit $N\to\infty$ and an associated continuum, the mean of the $N$ systems is the mean of a system determined by a Schrödinger equation (54), via an argument similar to Bohmian mechanics. The leading correction (32) to the limit is of order $O(N^{2/d})$ which goes exceedingly poorly to zero, making it likely that for reasonable $N$ the errors are always large.
The proposed experiments take small $N$ and assume these systems are actual multiparticle systems in traditional configuration space.

I don't think he actually showed anything like what he claimed, since the universe is a single system and not an ensemble of subsystems. The splitting into subsystems, which for Smolin is God-given and must be fixed to define the interaction, is arbitrary in our actual universe. Hence there is no way to test his theory.
Smolin interpretation is so superior because its background independent
Smolin's definitions are based on the Euclidean norm in configuration space, hence assume a flat background.

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A. Neumaier

Smolin reasoned [...]

There are two kinds of realists.
1. Naive realists
2. Magical realists.

Both answered yes to these two questions:

"First off, does the natural world exist independently of our minds? More precisely, does matter have a stable set of properties in and of itself, without regard to our perceptions and knowledge?

Second, can those properties be comprehended and described by us? Can we understand enough about the laws of nature to explain the history of our universe and predict its future?"

I want to know where Neumaier belonged to.
Smolin's classification is too black and white.

According to the thermal interpretation of quantum physics, Nature existed before human minds existed, and had now and then objective properties comprehended and described locally by q-expectations of quantum fields and nonlocally by more complicated q-expectations. Perceptions and knowledge only provide approximations to these objective properties, more knowledgeable people having better approximations about aspects where they are knowledgeable.. We can explain part of the history and predict part of the future since our knowledge and understanding of the true state of the universe is limited.

In contrast to Smolin, the TI does not need to take any limits to recover the quantum laws, except to the extent it is needed to get standard quantum mechanics from standard quantum field theory.

jlcd

I now read Smolin's Quantum mechanics and the principle of maximal variety, which contains the technical material. He proposes a theory with an ensemble of $N$ identically structured systems in a $d$-dimensional multiparticle configuration space interacting with each other via a strange, messy multiparticle action (19), which is mathematically ill-defined since the complex logarithm is multivalued.

He shows that in the limit $N\to\infty$ and an associated continuum, the mean of the $N$ systems is the mean of a system determined by a Schrödinger equation (54), via an argument similar to Bohmian mechanics. The leading correction (32) to the limit is of order $O(N^{2/d})$ which goes exceedingly poorly to zero, making it likely that for reasonable $N$ the errors are always large.
The proposed experiments take small $N$ and assume these systems are actual multiparticle systems in traditional configuration space.

I don't think he actually showed anything like what he claimed, since the universe is a single system and not an ensemble of subsystems. The splitting into subsystems, which for Smolin is God-given and must be fixed to define the interaction, is arbitrary in our actual universe. Hence there is no way to test his theory.

Smolin's definitions are based on the Euclidean norm in configuration space, hence assume a flat background.
It's related to Smolin idea that time is fundamental, space is emergent. Look. Smolin book has thousands of facts. It may be the greatest quantum book of the century for the masses ever. If you will google "Smolin realist vs antirealist". You will see many physicists read it. So hope you can read it too. The following is (I promise) the last passages (very critical) that I need to share so we can properly scrutinize whether time is really fundamental and space emergent. As his relational hidden variables is based on this:

(can anyone refute the following?)

This is as far as principles take us. The next step is to frame hypotheses. I propose three hypotheses about what lies beyond spacetime and beyond the quantum:

Time, in the sense of causation, is fundamental. This means the process by which future events are produced from present events, called causation, is fundamental.

Time is irreversible. The process by which future events are created from present events can’t go backward. Once an event has happened, it can’t be made to un-happen.*

Space is emergent. There is no space, fundamentally. There are events and they cause other events, so there are causal relations. These events make up a network of relationships. Space arises as a coarse-grained and approximate description of the network of relationships between events.

This means that locality is emergent. Nonlocality must then also be emergent.

If locality is not absolute, if it is the contingent result of dynamics, it will have defects and exceptions. And indeed, this appears to be the case: how else are we to understand quantum nonlocality, particularly nonlocal entanglement? These, I would hypothesize, are remnants of the spaceless relations inherent in the primordial stage, before space emerges. Thus, by positing that space is emergent we gain a possibility of explaining quantum nonlocality as a consequence of defects which arise in that emergence.2

The combination of a fundamental time and an emergent space implies that there may be a fundamental simultaneity. At a deeper level, in which space disappears but time persists, a universal meaning can be given to the concept of now. If time is more fundamental than space, then during the primordial stage, in which space is dissolved into a network of relations, time is global and universal. Relationalism, in the form in which time is real and space is emergent, is the resolution of the conflict between realism and relativity.

Let’s give a name to this version of relationalism, which emphasizes the reality and irreversibility of time and the fundamentality of the flow of present moments. Let’s call it temporal relationalism. We can contrast it with eternalist relationalism, which investigates the hypothesis that space is fundamental, but time is emergent.

RELATIONAL HIDDEN VARIABLES

We thus seek a completion of quantum mechanics which is background independent and relational, and which is framed in a world where time is fundamental and space is emergent. If it involves hidden variables, these must express relations between particles. Thus, the hidden variables do not give us a more complete description of an individual electron; they must describe relations which hold between one electron and other electrons. We can call these relational hidden variables.

A. Neumaier

It's related to Smolin idea that time is fundamental, space is emergent.
He says space is emergent but assumes for his dynamics the Euclidean distance in configuration space, which has no meaning unless space is assumed to be 3D Euclidean.
You will see many physicists read it.
His paper is 3 years old but only 8 times cited - hence probably not much read by experts.

No matter what you think and who read the book, the proposal in his paper, on which his book is based according to him, is deeply flawed.

jlcd

He says space is emergent but assumes for his dynamics the Euclidean distance in configuration space, which has no meaning unless space is assumed to be 3D Euclidean.

His paper is 3 years old but only 8 times cited - hence probably not much read by experts.

No matter what you think and who read the book, the proposal in his paper, on which his book is based according to him, is deeply flawed.
I think Smolin has reasons for everything. Hope others can share his (technical) reasons.

Note Smolin is no ordinary person. He is the one of the most powerful quantum gravitists in existence having developed loop quantum gravity. He thought of it since 1983. It's been 40 years so I think he has reasons.

I'm very interested in Smolin stuff now because I'm interested in the idea spacetime and matter are all emergent. And Smolin is just grasping at the effective theory.

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jlcd

He says space is emergent but assumes for his dynamics the Euclidean distance in configuration space, which has no meaning unless space is assumed to be 3D Euclidean.
Smolin had written a paper with Fotini Markopoulou that addressed this. See https://arxiv.org/pdf/gr-qc/0311059.pdf "Quantum Theory from Quantum Gravity" This reference was in his book.

His paper is 3 years old but only 8 times cited - hence probably not much read by experts.

No matter what you think and who read the book, the proposal in his paper, on which his book is based according to him, is deeply flawed.

PeterDonis

Mentor
Look. Smolin book has thousands of facts. It may be the greatest quantum book of the century for the masses ever.
Science is not done by writing books for the masses. It is done by constructing models that make testable predictions, and seeing whether the models pass the tests in actual experiments. Unless and until some tests are actually performed based on whatever testable predictions Smolin makes, his ideas will remain speculative hypotheses.

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Algebra i logika
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 Categoricity for primitive recursive and polynomial Boolean algebrasP. E. Alaev 389 Some absolute properties of $A$-computable numberingsS. A. Badaev, A. A. Issakhov 426 Generic amplification of recursively enumerable setsA. N. Rybalov 448 Theories of relatively free solvable groups with extra predicateE. I. Timoshenko 456 Universal functions and unbounded branching treesA. N. Khisamiev 476 Communications Positive presentations of families in relation to reducibility with respect to enumerabilityI. Sh. Kalimullin, V. G. Puzarenko, M. Kh. Faizrakhmanov 492 Sessions of the Seminar “Algebra i Logika”, Extended Sessions of the Seminar within the Framework of the Conference “Mal'tsev Readings” (November 20–23, 2017) 499


text:
# II.2.2

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### Wikia is a free-to-use site that makes money from advertising. We have a modified experience for viewers using ad blockers Wikia is not accessible if you’ve made further modifications. Remove the custom ad blocker rule(s) and the page will load as expected.

This problem has Hartshorne Height 2 and volume 2. II.2.1 can be used to solve this.

### HAPPY

For $x \in U \subset X$ know there is an affine containing $x$.

• Use that distinguished affines form a base for the topology(bottom page 70 Hartshorne) of affines to show something like $x \in D_f \subset \mbox{Spec} A \subset X$ and $D_f \subset U$.
• The result follows from II.2.1.


text:
class braket.task_result.photonic_model_task_result_v1.PhotonicModelTaskResult[source]

The photonic model task result schema

braketSchemaHeader

Schema header. Users do not need to set this value. Only default is allowed.

measurements (List[List[List[int]]]

List of lists of lists of int, where each int is bound between 0-255. Default is None.

taskMetadata

additionalMetadata