This fact was recognized in a paper that Heisenberg himself published in 1940 honoring Max Planck.

In fact, gravity is in many ways a much better quantum field theory than the Standard Model, since it appears to be valid all the way up to its cutoff at the Planck scale.

They rely on the fact that Planck's law, which relates temperature to the intensity of radiation emitted at individual wavelengths, can be solved for temperature if Planck ’ s statement of the intensities at two different wavelengths is divided.

However, the pioneering work of Max Planck ( 1858 – 1947 ) in the field of quantum physics suggests that there is, in fact, a minimum distance ( now called the Planck length, 1. 616 × 10 < sup >− 35 </ sup > metres ) and therefore a minimum time interval ( the amount of time which light takes to traverse that distance in a vacuum, 5. 391 × 10 < sup >− 44 </ sup > seconds, known as the Planck time ) smaller than which meaningful measurement is impossible.

In fact, physicists can choose their units so that the physical constants c, G, ħ = h /( 2π ), 4πε < sub > 0 </ sub >, and k < sub > B </ sub > take the value one, resulting in every physical quantity being normalized against its corresponding Planck unit.

However, he complained about the fact that Planck ( 1907 ) did not mention his earlier 1904-results ( like the dependency of apparent mass on temperature ).

What made the situation in the 1940s so desperate and gloomy, however, was the fact that the correct ingredients ( the second-quantized Maxwell-Dirac field equations ) for the theoretical description of interacting photons and electrons were well in place, and no major conceptual change was needed analogous to that which was necessitated by a finite and physically sensible account of the radiative behavior of hot objects, as provided by the Planck radiation law.

This follows from the fact that the Planck length is a reduced Compton wavelength equal to half the Schwarzschild radius of the Planck mass:

It was also subtly familiar, for it was the odor of the human body, but multiplied innumerable times because of the fact that the aborigines never bathed.

They lived in the same house and it didn't seem to be such a hard thing to do, but the sad realities of Lilly's life and the fact that Meltzer didn't love her never satisfied my wishful thinking.

Also, reserve the right to demand proof of death despite the fact that you'll probably never use it.

The adherence of many in the population to the Indian background in their pedigree, and emphasis upon the fact that their ancestors had never been slaves, becomes of prime interest in determining how far these elements promote the self-image of the intermediate status of the group in society.

She never hid the fact that she liked to play.

) The sorry fact about this young man, who was barely of age when he broke into major-league baseball, was that he really was a better ball player than he was given credit for being -- never so good as he claimed, and always an irritant to his associates, but a good steady performer when he could fight down the temptation to orate on his skills or cut up in public.

Although he never gets to play while the clock is running, he gets a big kick -- several every Saturday, in fact -- out of football.

But one does not have to affirm the existence of an evil order irredeemable in that sense, or a static order in which no changes will take place in time, to be able truthfully to affirm the following fact: there has never been justitia imprinted in social institutions and social relationships except in the context of some pax-ordo preserved by clothed or naked force.

From the time he had been at college he had achieved a certain tranquility and composure by accepting the fact that there were certain things he could never know.

The trouble with them was that they almost never worked, and in fact an agreement `` in principle '' historically turned out to be a sure sign that neither party really wanted the quarrel settled.

Kant is not generally considered to be a modern anthropologist, however, as he never left his region of Germany nor did he study any cultures besides his own, and in fact, describes the need for anthropology as a corollary field to his own primary field of philosophy.

It is in fact a private memento, and for this reason it is never awarded to either England or Australia, but is kept permanently in the MCC Cricket Museum where it can be seen together with the specially made red and gold velvet bag and the scorecard of the 1882 match.

However, despite the fact that he never officially bore the name Octavianus, to save confusing the dead dictator with his heir, historians often refer to the new Caesar — between his adoption and his assumption, in 27 BC, of the name Augustus — as Octavian.

The Lesbian or Aeolic school of poetry " reached in the songs of Sappho and Alcaeus that high point of brilliancy to which it never after-wards approached " and it was assumed by later Greek critics and during the early centuries of the Christian era that the two poets were in fact lovers, a theme which became a favourite subject in art ( as in the urn pictured above ).

This was not, however, the point in which Alfred came to be known as King of England ; in fact he would never adopt the title for himself.

He predicts that this man will be able to divine the color of this particular shade of blue, despite the fact that he has never experienced it.

It has been argued that the name " Titus " in 2 Corinthians and Galatians is nothing more than an informal name used by Timothy, implied already by the fact that even though both are said to be long-term close companions of Paul, they never appear in common scenes.

The fact that Bede never mentioned a special title for the kings in his list implies that he was unaware of one.

* Some disappearances had, in fact, never happened.

A 2nd century CE Greek known as Heraclitus the paradoxographer --- not to be confused with the 5th century BCE Greek philosopher Heraclitus --- claimed Euhemeristically that Cerberus had two pups which were never away from their father, as such Cerberus was in fact a normal ( however very large ) dog but artists incorporating the two pups into their work made it appear as if his two children were in fact extra heads.

A distinction is sometimes drawn between syntactic garbage, those objects the program cannot possibly reach, and semantic garbage, those objects the program will in fact never again use.

Named for William Legge, 2nd Earl of Dartmouth — an important supporter of Eleazar Wheelock's earlier efforts but who, in fact, opposed creation of the College and never donated to it — Dartmouth is the nation's ninth oldest college and the last institution of higher learning established under Colonial rule.

This conquest never happened, but some historians believe that the crossing referred to was in fact a small-scale exploratory or punitive expedition to Ireland.

In fact Germany never distinguished between the two types, giving them pennant numbers in the same series and never giving names to destroyers.

So far as I am concerned, the child is unmistakably father to the man, despite the obvious fact that child and father differ greatly -- sometimes for the better and sometimes for the worse.

However, it determined that neither this factor, nor `` the fact that all concerned in high executive posts in both companies acted honorably and fairly, each in the honest conviction that his actions were in the best interests of his own company and without any design to overreach anyone, including Du Pont's competitors '', outweighed the Government's claim for relief.

The fact that Sloan was an extrovert, concerned primarily with what he saw, adds greatly to the value of his art as a human chronicle.

He is concerned, however, with the fact that the promise is not being fulfilled to the seed of Abraham ( referring to the Jews ).

Of those who did, Cukor preferred Paulette Goddard, but her supposedly illicit relationship with Charlie Chaplin ( they were, in fact, secretly married ) concerned Selznick.

The drinks themselves are not the same, and vary between the Sivolvian " chinanto / mnigs " which is ordinary water served at slightly above room temperature, and the Gagrakackan " tzjin-anthony-ks " which kills cows at a hundred paces ; and in fact the one common factor between all of them, beyond the fact that the names sound the same, is that they were all invented and named before the worlds concerned made contact with any other worlds.

The encyclical acknowledges that " perhaps not everyone will easily accept this particular teaching ", but points out that the Roman Catholic Church cannot " declare lawful what is in fact unlawful ", because she is concerned with " safeguarding the holiness of marriage, in order to guide married life to its full human and Christian perfection.

That same year, sitting in a library in New Orleans while his father took medical courses at a nearby college, Howard discovered a book concerned with the scant fact and abundant legends surrounding an indigenous culture in ancient Scotland called the Picts.

According to Albert Sturtevant, " far as the element Rata-is concerned, Bugge's hypothesis has no valid foundation in view of the fact that the Norse word Rata ( gen. form of Rati *) is used in

He did not address the fact that Whorf was not principally concerned with translatability, but rather with how the habitual use of language influences habitual behavior.

Critics pointed out that a precedent had been set in the naming of einsteinium during Albert Einstein's life and a survey indicated that chemists were not concerned with the fact that Seaborg was still alive.

The marriage of these two observations depends on the fact that each of them is essentially concerned with time.

Though neither side intended to start a nuclear war, and, in fact, were extremely concerned about the possibility of it, neither side adopted strategies to calm things down, so sure were they of their adversaries ' bad faith.

In fact, the case discusses the hardships collectively faced by all of the children concerned.

One theory has been that he was concerned that if he was to abandon Joan, he might also lose Burgundy ; another theory suggests that his slightly " formulaic " love letters to his wife should be taken at face value, and that he was in fact very deeply in love.

In fact, Carson had become concerned about the effect of pesticides, DDT particularly, as early as the 1940s, when anti-pest campaigns had been part of the Pacific war effort.

The fact that the man is literally, as far as the audience is concerned, thrown into existence brings to mind the Heideggerian concept of Geworfenheit (‘ Throwness ’).” Heidegger is clearly using the expression metaphorically as is Beckett ; the man is expelled from a womb-like condition, from non-being into being.

Much of season seven is concerned with Kara's attempts to adjust to life on Earth, especially after learning of Krypton's destruction and the fact that her ' younger ' cousin is now at least the same age as her.

The " fake fumble " is in fact a real one as far as the rules are concerned, and if the defense manages to get the ball, the coach's judgement is likely to be questioned by fans and media alike.

" In fact, he was so concerned for Bath, he visited the town on four occasions between 1747 and 1762 to preach the gospel.

He should have been concerned about his age, for he was rejected despite the fact that his scores were well above the scores of an average admittee at University of California Davis medical school.

Despite Pickford's embrace of the new medium it seems she was as concerned as everyone else about how her voice would record, despite the fact she had a stage career before entering film.

" She further states that " The Special Rapporteur is concerned that this latest development indicates that the situation with regard to religious minorities in Iran is, in fact, deteriorating.

As far as the word is concerned it may probably not antedate the fourth century, when it was introduced in the Church at Carthage ; but the fact is certainly older.