“We show that some known classical results have particularly simple derivations within the Ashtekar formalism. These include Witten's positive energy theorem…”

"Positive energy in quantum gravity" arXiv (Jun 10, 2014)

Adopted from Wikiquote. Last update June 3, 2021. History

Help us to complete the source, original and additional information

Do you have more details about the quote "We show that some known classical results have particularly simple derivations within the Ashtekar formalism. These inc…" by Lee Smolin?

Lee Smolin52

American cosmologist 1955

Related quotes

“Calculation establishes that a quantum positive energy theorem may be possible using a representation based on the Ashtekar connection. Left open is a key question of whether this use of the Ashtekar connection is necessary or whether a positive quantum energy result can be achieved for representations based on other connections, i. e., for [other] values of the Immirzi parameter.”

Lee Smolin (1955) American cosmologist

"Positive energy in quantum gravity" arXiv (Jun 10, 2014)

“One of the evident facts about the world is the stability of empty space-time. In classical general relativity we can explain this as a consequence of the positive energy theorem… the positive energy theorem must extend in some suitable form to any viable quantum theory of gravity.”

Lee Smolin (1955) American cosmologist

"Positive energy in quantum gravity" arXiv (Jun 10, 2014)

“The positive energy theorem was for half a century or more an open challenge to relativists. Many attempts were made to prove flat spacetime was stable, but none completely succeeded completely until a majestic tour de force of geometric reasoning of Shoen and Yau. This was followed two years later by a proof of Witten, which was as elegant as it was short. It is this proof of Witten’s that we take as a template here for the quantum theory.”

Lee Smolin (1955) American cosmologist

"Positive energy in quantum gravity" arXiv (Jun 10, 2014)

“Other qualities of bodies are connected with simple energy of motion and energy of position. Such is heat, which we find by experiment can be turned into work. Finding it convertible with energy, we call it a form of energy. ...But as to heat, it is further established by experiment that in this case the energy of motion does really persist as such. Thus a gas consists of molecules flying about with velocity, rotating and vibrating, and so having energy motion. All this energy of motion is what we call heat, and thus heat is a repetition of a known meaning of energy. Again, heat exists between a radiating body and the thing it warms; now the intermediate space is filled by the luminiferous ether, which, being elastic, has in its ultimate parts both energy of motion energy of position. In these forms the heat exists in the space in question.”

William Kingdon Clifford (1845–1879) English mathematician and philosopher

"Energy and Force" (Mar 28, 1873)

“In Greece, the position at the outset was particularly difficult, so now we have to be particularly patient with the country. That's no surprise.”

Mario Draghi (1947) Italian banker and economist

spiegel.de http://www.spiegel.de/international/europe/spiegel-interview-with-ecb-president-mario-draghi-a-941489.html.

“What channels the energy of our total being to produce anything that might be within the boundaries of possibility is known as will.”

Carlos Castaneda (1925–1998) Peruvian-American author

Source: The Eagle's Gift, (1981)

“When the Löwenheim-Skolem theorem is applied to particular formal systems, we obtain as special cases: Every group, field, ordered field, etc., has a countable subsystem of the same type. A more spectacular result follows from applying the theorem to set theory (a system which we shall later formalize): There is a countable collection of sets, such that if restrict the membership relation to these sets alone, they form a model for set theory (more precisely all the true statements of set theory are true in this model). In particular, within this model which we may denote by M, there must be an uncountable set. This paradox, that a countable model can contain an uncountable set, is explained by noting that to say a set is uncountable merely asserts the nonexistence of a one-one mapping of the set with the set of integers. The "uncountable" set in M set actually has only countably many members in M, but there is no one-one correspondence \underline {within} M of this set with the set of integers.”

Paul Cohen (1934–2007) American mathematician

Set theory and the continuum hypothesis, pp. 19–20 https://books.google.com/books?id=Z4NCAwAAQBAJ&pg=PA19 <br class="br">Set Theory and the Continuum Hypothesis (1966)

“When a body is let fall from a higher position to lower one, it has, at the instant when it is let go, energy of motion; but it gains, in falling, as much energy of motion as it loses energy of position. It is found that the sum of energy of motion and energy of position is always constant. ...Energy is a quantity which can be greater or less but has no direction. ...This constancy is expressed by including them in common name of Energy, and saying that energy is conserved, or is indestructible. This form of speech might be applied to other cases of alternate immortality, where one of two things comes into existence on disappearance of the other.”

William Kingdon Clifford (1845–1879) English mathematician and philosopher

"Energy and Force" (Mar 28, 1873)

“The idea that theorems follow from the postulates does not correspond to simple observation.”

Richard Hamming (1915–1998) American mathematician and information theorist

The Unreasonable Effectiveness of Mathematics (1980)
Context: The idea that theorems follow from the postulates does not correspond to simple observation. If the Pythagorean theorem were found to not follow from the postulates, we would again search for a way to alter the postulates until it was true. Euclid's postulates came from the Pythagorean theorem, not the other way around.

“Some people are constructive, if you like. Others are destructive. It's this diversity in humankind that results in some making positive contributions and some negative contributions. It's necessary to have enough who make positive contributions to overcome the problems of each age.”

Jonas Salk (1914–1995) Inventor of polio vaccine

Academy of Achievement interview (1991)

“We show that some known classical results have particularly simple derivations within the Ashtekar formalism. These include Witten's positive energy theorem…”

Help us to complete the source, original and additional information

Lee Smolin52

Related quotes

Related topics