Einstein's purely algebraic physics and "my entire castle in the air"

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jake jot
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Can someone show or illustrate how purely algebraic physics can describe black holes, gravitational waves or other predictions of General Relativity?

In a letter of Einstein to Paul Langevin, 3 October 1935, as translated in Stachel 1986, 379-80, he wrote:

"In any case one does not have the right today to maintain that the foundation must consist in a field theory in the sense of Maxwell. The other possibility, however, leads in my opinion to a renunciation of the time-space continuum and to a purely algebraic physics. Logically this is quite possible (the system is described by a number of integers; “time” is only a possible viewpoint [Gesichtspunkt], from which the other “observables” can be considered—an observable logically coordinated to all the others. Such a theory doesn’t have to be based upon the probability concept. For the present, however, instinct rebels against such a theory"


And Einstein wrote in a letter to his friend Besso in 1954, “I consider it quite possible that physics cannot be based on the field concept, i.e., continuous structure. In that case, nothing remains of my entire castle in the air, gravitation theory included, (and of) the rest of modern physics”

What does he mean by continuous structure? Was he talking about QFT? If it couldn't be based on field concept, then what is it? And why would it lead to breakdown of all of modern physics?
 
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  • #2
robwilson
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Can someone show or illustrate how purely algebraic physics can describe black holes, gravitational waves or other predictions of General Relativity?

In a letter of Einstein to Paul Langevin, 3 October 1935, as translated in Stachel 1986, 379-80, he wrote:

"In any case one does not have the right today to maintain that the foundation must consist in a field theory in the sense of Maxwell. The other possibility, however, leads in my opinion to a renunciation of the time-space continuum and to a purely algebraic physics. Logically this is quite possible (the system is described by a number of integers; “time” is only a possible viewpoint [Gesichtspunkt], from which the other “observables” can be considered—an observable logically coordinated to all the others. Such a theory doesn’t have to be based upon the probability concept. For the present, however, instinct rebels against such a theory"


And Einstein wrote in a letter to his friend Besso in 1954, “I consider it quite possible that physics cannot be based on the field concept, i.e., continuous structure. In that case, nothing remains of my entire castle in the air, gravitation theory included, (and of) the rest of modern physics”

What does he mean by continuous structure? Was he talking about QFT? If it couldn't be based on field concept, then what is it? And why would it lead to breakdown of all of modern physics?
It is always worth listening to Einstein. Even if he predicts the demise of [the whole of] modern physics. All of modern physics is based on geometry, and Einstein is suggesting an algebraic approach instead. The basic idea is that instead of using SU(2) to describe spin, you just use the quaternion group Q_8. So instead of having a continuous magnetic field as in the classical theory, you just have a bunch of discrete spins. A great deal can be done with this approach, but I don't know that anyone has got as far as describing black holes or gravitational waves. First they would need to develop an algebraic quantum theory of gravity.
 
  • #3
mitchell porter
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The basic idea is that instead of using SU(2) to describe spin, you just use the quaternion group Q_8. So instead of having a continuous magnetic field as in the classical theory, you just have a bunch of discrete spins. A great deal can be done with this approach, but I don't know that anyone has got as far as describing black holes or gravitational waves.
This reminds me of the claim that 2+1 dimensional gravity in AdS space, for a particular AdS radius, is holographically dual to the Ising model (more specifically, dual to the CFT describing the critical point of the Ising model). Is there a three-dimensional counterpart of using Q_8 to describe spin?
 
  • #4
robwilson
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This reminds me of the claim that 2+1 dimensional gravity in AdS space, for a particular AdS radius, is holographically dual to the Ising model (more specifically, dual to the CFT describing the critical point of the Ising model). Is there a three-dimensional counterpart of using Q_8 to describe spin?
Do you mean 3 as in 2+1 or as in 3+1? I use Q_8 in 3+1 dimensions, and I don't see any counterpart in 2+1 dimensions.
 
  • #5
jake jot
302
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It is always worth listening to Einstein. Even if he predicts the demise of [the whole of] modern physics. All of modern physics is based on geometry, and Einstein is suggesting an algebraic approach instead. The basic idea is that instead of using SU(2) to describe spin, you just use the quaternion group Q_8. So instead of having a continuous magnetic field as in the classical theory, you just have a bunch of discrete spins. A great deal can be done with this approach, but I don't know that anyone has got as far as describing black holes or gravitational waves. First they would need to develop an algebraic quantum theory of gravity.

What about Einstein castle in the air? Einstein wrote in a letter to his friend Besso in 1954

“I consider it quite possible that physics cannot be based on the field concept, i.e., continuous structure. In that case, nothing remains of my entire castle in the air, gravitation theory included, (and of) the rest of modern physics”

What does he mean by continuous structure? Was he talking about QFT? How is this related to algebra vs geometry? If it couldn't be based on field concept, then what is it? And why would it lead to breakdown of all of modern physics?
 
  • #6
Fra
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What does he mean by continuous structure? Was he talking about QFT? If it couldn't be based on field concept, then what is it? And why would it lead to breakdown of all of modern physics?
Can's speak for Einsteins of course but a guess based on the fact that the constructive principles of relativity is that its the relations between observations communicated between observers that is a key; not wether one can embed or index these things in a continuum. Ie. spacetime is defined in terms of relations between matter, ie it makes no sense to talk about spacetime in itself, unless it is defined in terms of matter. The spacetime itself could well just be a extrapolated mathematical embedding into the continum, that lacks physical justification.

In a sense one can associate an algebraic approch to measurment theory as, starting with the set of all possible measurements. The problem is that the linear operators of QM and QFT are defined on fields, but perhaps one can make it more abstract and consider only the operation in terms of internal structure, and instead of thinking of the transformations or operations as changing of the physical states and distributed fields, one can see it as the change of the observers state (which only at equilbrium would have a holographic duality with the outside world). ie. the internal code comes first(microstructure of matter), and the holohraphic illusion later(fields in spacetime).

But this would suggest a reconstruction of modern QFT indeed, because we do not know howto speak about microstructure about matter, without the QFT baggage and spacetime.

Similar critique appears also on probabilistic foundations, when one tries to make "inside ratinngs" without having available massive statistics, in this reconstruction of a theory of degree of beliefe, introducing the real numbers may be premature. Its not that its "wrong", its just too much, and this later causes problems during quantization as mathematical possibilities of embeddin are confussed with physically justified possibilities.

/Fredrik
 

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