View allAll Photos Tagged Discretization
Church of St Mary
Tomb of Baron William Bardolf and Lady Joan. Alabaster. Chapel of St Margaet, South aisle. Commissioned by Baron William around 1437, probably completed by 1447
Condition: the figures have suffered minor vandalism, but the colour of their robes has been restored discretely; figures have been removed from the now empty niches of the tomb chest
The tomb is set in St Margaret’s chapel, striking for its richly decorated parclose screen, mirrored in that of the chapel dedicated to the Virgin to the north. In 1437 Baron William established a chantry in the chapel, and in his will of 1438 arranged for his burial there. The tomb may have been in place by 1447, the date of Lady Joan’s will, in which she also arranged to be buried in the chapel.
The effigies are the best preserved of the pre-Reformation alabaster tombs in East Anglia
Baron William and Lady Joan recline with their hands clasped in prayer, looking up to heaven. Baron William rests his feet on the wings of an improbably duck-like eagle, while Lady Joan’s feet touch a fierce dragon, the emblem of St Margaret, to whom the chapel is dedicated. Baron William’s head is crowned by a chaplet and rests on his tilting helmet, while Lady Joan’s is on a pillow accompanied by two smaller angels. The effigies are well handled; the flow of her robes and tassels for the cloak are contrasted with the detail of his armour and gloves and both wear the SS livery collar, while he has the garter with the inscription ‘HONI SOIT QUI MAL Y PENSE’ on a blue ribbon on his left leg. The SS livery collar was not an insignia but a popular sign of allegiance, associated during the early fifteenth century with the House of Lancaster.
The splendour of the tomb reflects Baron Bardolf’s position; born William Phelip in 1383/4, on his mother’s side he was the grandson of the most powerful figure in East Anglia, Sir Thomas Erpingham, which, in the account in the ODNB, shaped his career.
Baron William had been lord of Dennington manor, which by the sixteenth century had passed to Sir Richard Wingfield, who sold it to Anthony Rous in 1538. There is a wall monument to Sir Thomas Rous (d.1619) kneeling in prayer opposite his wife on the south wall of the chapel, but by the mid seventeenth century Dennington Manor had been destroyed and Henham Hall, a large Tudor house built in 1538, which Anthony Rous had bought in 1548, became the seat of the Rous family (later ennobled as Earls of Stradbroke).
Richard and Sarah Cocke, The Public Sculpture of Norfolk and Suffolk, Liverpool University Press for the Public Monuments and Sculpture Association, 2013, pp.258-259
detail of Baron William Bardolf
Discrete & sophisticated are the defining features of this dress & skirt. At first glance it's a sleek close fitting coat, but look again, the sleeves are integrated so while your fingertips peep out your arms are held down. The coat has a concealed zip and buttons up, under the nose (can hide a gag for those quiet days) so once you're in, you're in.
This is paired with a extra narrow skirt for when you're not in any hurry.
The Sony RX0 is about the size of a matchbox so it is very discrete but it is not really suitable for indoor photography and this is why the images are a bit noisey
In 1974 St. Saviour’s became the parish church for the surrounding area and in 2000 was made the Studium for the formation and training of priests for the Irish Dominicans. A further major step in these years was the establishment of the Dominican Polish Chaplaincy in St. Saviour’s which today sees large numbers of Polish faithful attending Mass and services every week, along with the Irish and Spanish-language congregations, making St. Saviour’s a truly international church in the heart of Dublin.
All Hallows London Wall, London
Also known as All Hallows on the Wall, this little church sits discretely with its back turned near Liverpool Street station. The medieval church it replaced was actually built into the wall, but was demolished for road-widening. Simon Bradley points out that the 18th Century replacement by George Dance uses part of the wall for its foundation on the north side. As at Dance's other church nearby, St Botolph Aldgate, there is a trim liveliness to the exterior which is confident without being prim. Dance knew what worked best for Wren, what worked best for Hawksmoor, and he was no iconoclast.
All Hallows is somewhat overshadowed by its monstrous neighbours, but nevertheless gives them a run for their money. It sits like a small bastion, a gatehouse if you like, guarding the financial citadels of Bishopsgate - or perhaps, warning you off of them. The interior is said to be lovely, but I have yet to see inside, as like most of the other churches in this group on and around Bishopsgate* it is hardly ever open.
*Don't let this comment put you off of St Botolph Bishopsgate, which is open every day, Monday to Friday. Unfortunately, St Helen Bishopsgate, St Ethelburga Bishopsgate, St Peter Cornhill, St Katherine Cree and St Andrew Undershaft are not.
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As a concert photographer, the low profile and body hugging characteristics of my black Domke F-6 allows me to easily move around in the crowd in a discrete way. Much better than walking with a bulky padded photo backpack. To my surprise the F-6 even fits my D700 with a small prime lens, without having to take off the grip. Being a shoulder bag it enables me to change lenses even between shots without the risk of anything dropping on the floor. When I am taking a short break, I can rest my camera on it to spread the weight, and still walk around.
Here’s what’s inside my Domke:
- Nikon D700 with MB-D10 grip and Nikkor 50mm F1.4G AF-S
- Tamron 28-75mm F2.8
- Nikkor 35mm F1.8DX (yes it’s a DX, but until I can afford the 35mm F1.4G I abuse it on my FX D700, works fine within limits)
- Zenitar 16mm F2.8 fisheye
- Nikon SB800 speed light, omnibounce, tripod adapter (for backstage/band portraits and the really really dark venues)
- Yongnuo 622n TX radio flash trigger commander + Yongnuo 622n receiver to remote trigger the speed light
- Manfrotto Pixi mini tripod (I can put the speedlight on it for more directional control and stability)
- Spare CF memory card
- Microfiber towel and air blower, for dusty venues and flying beer spatters
- Gerber LX flashlight, wound with a bit of gaffer tape since almost everything happens in the dark, and you can never go wrong with a bit of gaffer tape
- Custom hearing protection ear plugs and spare foamies, ears are priceless
...in the grass, the beetle spied the mannequin searching for her head.
(from the first test roll of a Brownie Twin 20)
With discrete route branding added. Good to see that Ipswich Buses have refrained from plastering the side of these recently renovated vehicles with those large and hideous graffiti type route numbers. I'm still not a huge fan of this livery, but at least the bus looks clean and smart.
Sleeves join to the body and ties at the knee for discrete confinement. Huge hood finishes this delicious garment
Living up to its name, this butterfly is the commonest blue found in the British Isles. While the male has bright blue uppersides, the female is primarily brown, with a highly variable amount of blue. This is the most widespread Lycaenid found in the British Isles and can be found almost anywhere, including Orkney. It is absent, however, from Shetland and the mountainous areas of Wales and Scotland. This butterfly forms reasonably discrete colonies measured in tens or hundreds, with individuals occasionally wandering some distance.
Shortly after first light in Lancashire. Low level discrete photography.
If it's worth a fave, then surely a comment too
The oystercatchers are a group of waders forming the family Haematopodidae, which has a single genus, Haematopus. They are found on coasts worldwide apart from the polar regions and some tropical regions of Africa and South East Asia. The exception to this is the Eurasian oystercatcher and the South Island oystercatcher, both of which breed inland, far inland in some cases.
In the past there has been a great deal of confusion as to the species limits, with discrete populations of all black oystercatchers being afforded specific status but pied oystercatchers being considered one single species.
The name oystercatcher was coined by Mark Catesby in 1731 as a common name for the North American species H. palliatus, described as eating oysters. Yarrell in 1843 established this as the preferred term, replacing the older name sea pie.
The genus name Haematopus comes from the Greek haima αἳμα blood, pous πούς foot.
The different species of oystercatcher show little variation in shape or appearance. They range from 39–50 cm (15–20 in) in length and 72–91 cm (28–36 in) in wingspan. The Eurasian oystercatcher is the lightest on average, at 526 g (1.160 lb), while the sooty oystercatcher is the heaviest, at 819 g (1.806 lb).
The plumage of all species is either all-black, or black (or dark brown) on top and white underneath. The variable oystercatcher is slightly exceptional in being either all-black or pied. They are large, obvious, and noisy plover-like birds, with massive long orange or red bills used for smashing or prying open molluscs. The bill shape varies between species, according to the diet. Those birds with blade-like bill tips pry open or smash mollusc shells, and those with pointed bill tips tend to probe for annelid worms. They show sexual dimorphism, with females being longer-billed and heavier than males.
Feeding
The diet of oystercatchers varies with location. Species occurring inland feed upon earthworms and insect larvae. The diet of coastal oystercatchers is more varied, although dependent upon coast type; on estuaries bivalves, gastropods and polychaete worms are the most important part of the diet, whereas rocky shore oystercatchers prey upon limpets, mussels, gastropods, and chitons. Other prey items include echinoderms, fish, and crabs.
Breeding
Nearly all species of oystercatcher are monogamous, although there are reports of polygamy in the Eurasian oystercatcher. They are territorial during the breeding season (with a few species defending territories year round). There is strong mate and site fidelity in the species that have been studied, with one record of a pair defending the same site for 20 years. A single nesting attempt is made per breeding season, which is timed over the summer months.
The nests of oystercatchers are simple affairs, scrapes in the ground which may be lined, and placed in a spot with good visibility. The eggs of oystercatchers are spotted and cryptic. Between one and four eggs are laid, with three being typical in the Northern Hemisphere and two in the south. Incubation is shared but not proportionally, females tend to take more incubation and males engage in more territory defence. Incubation varies by species, lasting between 24–39 days. Oystercatchers are also known to practice "egg dumping." Like the cuckoo, they sometimes lay their eggs in the nests of other species such as seagulls, abandoning them to be raised by those birds.
Conservation
One species of oystercatcher became extinct during the 20th century, the Canary Islands oystercatcher. Another species, the Chatham oystercatcher, which is endemic to the Chatham Islands of New Zealand, is listed as endangered by the IUCN, and the African oystercatcher is considered near threatened. In the past there has been conflict with commercial shellfish farmers, but studies have found that the impact of oystercatchers is much smaller than that of shore crabs.
German postcard by Philips.
Austrian singer and actor Willy Hagara (1927-2015) was a popular film and TV star from the mid 1950s till the mid 1960s. The discrete and elegant Schlager star had five Top 10 hits, including the evergreen 'Casetta in Canada' (1958). The singer’s career did not survive the Beat wave, but in 1969 an inheritance made him a millionaire.
Wilhelm ‘Willy’ Hagara was born in Vienna, Austria in 1927. He was initially trained as a postal clerk and practiced this profession as well. In 1946, he won a popular song contest in the Wiener Konzerthaus. He focused all his activities to this new career, and took singing and acting lessons. During this time he was successful with folk songs and as the singer of the band of John Fehring, who later became the leader of the ORF Big Band Orchestra. Hagara was a classic band singer who performed one of his songs in an early Schlager show for the German ARD television, Schlager-Expreß/Schlager Express (1953). Finally in 1955 came his breakthrough with the song Eine Kutsche voller Mädels/A coach full of girls (1955). Willy Hagara moved to Frankfurt in Germany and he became something like the German Perry Como, whose songs in German versions he often would sing. Two years later he appeared in his first film, the musical comedy Weißer Holunder/White Elder (Paul May, 1957) with Germaine Damar. It was followed by a string of light entertainment films: Liebe, Mädchen und Soldaten/Love, girls and soldiers (Franz Antel, 1958), Mein ganzes Herz ist voll Musik/My whole heart is filled with music (Helmut Weiss, 1959), Der Haustyrann/The domestic tyrant (Hans Deppe, 1959) starring Heinz Erhardt, Laß mich am Sonntag nicht allein/Let me not be alone on Sunday (Arthur Maria Rabenalt, 1959) with Heidi Brühl, and Paprika/Pepper (Kurt Wilhelm, 1959).
Cinema attendance in Germany and Austria had spectacularly grown in the 1950s, but at the end of the decade it first stagnated and then went into freefall in the 1960s. The once so popular Schlager films became outdated. In 1961 Willy Hagara appeared in his last Schlager film, Ramona (Paul Martin, 1961) with Senta Berger. At the time, television was developing into a mass medium that could compete with the cinema. In 1962 there were already 7 million TV sets in West-Germany. Hagara moved over to the small screen and appeared in such musical TV comedies as Mitternachtszauber/Midnight Magic (Ralph Lotar, 1964) with Werner Fuetterer, and Vom Ersten das Beste/From the first the best (Ekkehard Böhmer, 1965) with Hannelore Auer. These TV productions were in the same genre as the films he had made in the 1950s for the cinema. Until the mid-1960s he starred in numerous TV films and sold many records. In total he had five Top 10 hits, including the evergreen Casetta in Canada. His song Du spielst 'ne tolle Rolle (You play a great role) became in the version of Nat King Cole a Top 10 hit in the US. But the Beat wave finished his singing career. His later TV-films included Ein Mädchen von heute/A girl of today (Dieter Finnern, 1966) with Karin Baal. In 1969 he got a million inheritance: his father, the merchant Franz Hagara, left him with a villa and several lease lands in Vienna. He did not retire, but he bridged the 1970s with performances during galas. Incidentally he appeared as a guest in such TV shows as Hit-Journal (H.B. Theopold, 1973), Tango-Tango (Horst Eppinger, 1976) and Ein kleines Glück auf allen Wegen/A small fortune on all routes (Ekkehard Böhmer, 1980). After the death of his wife in 1986, Willy Hagara retired from show business. His last public appearance was in a show from Schloss Schönbrunn in Vienna in 2002 on the occasion of his 75th birthday. Willy Hagara passed away in 2015 in Wiesbaden, Germany. He was 87.
Sources: Wälz Studer (Memoryradio.de) (German), Wikipedia (English and German), and IMDb.
And, please check out our blog European Film Star Postcards.
Auguste Rodin's large marble sculpture of two naked lovers fused in passion, known as Le Baiser...The Kiss.
Here, I chose to present just part of the famous sculpture, with discrete focus on their coupling. In my eyes, providing them some privacy for this most emotive moment.
Rodin's lovers appear timeless to me. A representation of infatuation, oblivious to all else. But their love was doomed. They are Paolo Malatesta and Francesca da Polenta (originally as reliefs from Rodin's monumental bronze Gates of Hell, based on Dante's Divine Comedy). They were discovered by Francesca's husband and killed by him.
The couple pass in to Hell, through the Circle of the Lustful, where the souls of sinners who gave themselves over to sexual pleasures are punished by being transformed in to a 'whirling cyclone'.
Three life-size versions of the sculpture were executed in Rodin's lifetime. The earliest is this one here in the collection of the Musée Rodin, within the Hôtel Biron, a magnificent 18th century palace that the sculptor used as his Paris studio until his death in 1917.
Le Baiser 1888. Marble 1.82m x 1.16 m x 121 m.
Link to exterior of Musée Rodin: www.flickr.com/photos/112623317@N03/51941066998/in/photol...
© All rights reserved.
The Essex Skipper forms discrete colonies that vary from a small number of individuals to several thousand. Where it occurs it can therefore be very common. This species is very similar in appearance to the Small Skipper and, because of this similarity, was not recognised as a separate species until 1889.
Breathless my heart is building a magic, a discrete tower of love...
Modelo: Gusy Bello
Franco Petrini Photography © 2010
newly weds can pose on the otherwise completely deserted beaches of Qingdao in the BaDaGuan area. Only them and a discrete photographer.
Obviously not as discrete as I thought as I was given the glare I am receiving but none the less it was a great little park where everyone was playing some sort of game. Great to witness! Captured on my 135mm Tamron with a little grain added for effect in LR6.
Point de Vue Pearl H.
Alors, je cible sans plus attendre le divan, afin de me faire discrète et à la fois observatrice. Depuis le début, je ressentais que je n'étais pas faite pour ces mondanités, mais peu m'importe sur l'instant. Dorénavant je suis là, je dois faire face, rester brave.
So, I target without further delay the couch, to make me discreet and at the same time observer. From the beginning, I felt that I was not made for these worldly, but I do not care about the moment. From now on I'm here, I have to face, stay brave.
Point de vue Griffith H.
Je l'a vois... Moi qui pensais être le seul enfermé dans ce contrat , me détends soudainement. Sa petite moue charmante en dit long sur son humeur... Mais elle est malgré tout, d'un charme inattendu. Le blond nordique de ses cheveux me captive, cette peau diaphane qui ne demande qu'à rosir de plaisir je n'en doute pas , et ses yeux d'un bleu semblable à une mer de glace. En quelques secondes, je suis d'un tout autre état d'âme. Je veux la voir s'esclaffer, je veux qu'elle me remarque et je veux être celui à qui elle pensera ce soir...
I saw her ... I, who thought I was the only one locked up in this contract, suddenly relax. Her charming little pout says a lot about her mood ... But she is still, of an unexpected charm. The Nordic blond of her hair captivates me, this diaphanous skin that just wants to blush with pleasure I do not doubt, and her eyes a blue like a sea of ice. In a few seconds, I am of a completely different state of mind. I want to see her laughing, I want her to notice me and I want to be the one to whom she will think tonight ...
White and blue Gladiolus flower macro fine art abstract on APS-C sensor using 28mm lens with extension tubes.
A few moths from last night, fairly mild but competing with a full moon. Still had a nice selection to look at in the morning including a few new ones on the roof terrace in L'Orxa, Alicante province.
You can see more of my moth images on my main website HM Wildlife Photography - Garden Moths or my other flickr account HM Wildlife
Hello and hope this finds you all fine, happy & healthy :)
Today, there's a rather sensitive subject to be touched here and I'll try to do that in the softest and most discrete of ways.
As you may have noticed, there appears a Grey Ribbon of Awareness at the end of the sentence.
This ribbon is to raise awareness about such issues as Mental Illness, Diabetes, Brain Cancer and Asthma.
Mental Illness is the subject to be dealt with today.
Those of you who are familiar with my profile are aware about my studies in Psychology.
I'd like to openly share here with you today the reason I took the time to complete these studies and also put them in praxis by undergoing a 7 year process of personal analysis, when in the first place I was ready to start my studies in Architecture and Interior Design.
Growing up I happened to be directly exposed to mental illness. For understandable reasons of descrition there'll be no commenting on who this person/people were.
The reason for coming out open with the subject is only one: to raise awareness.
So, let me say to you that mental illness is NOT a resposibility of the people who carry and live with it, but it is a whole lot of responsibility of the poeple living with such individuals to support them the right way - and this includes getting professional help.
I'm aware of the fact that mental illness stigmatises people and families and lives....and I'm also aware that pychologists and therapists are not the most favorited people of all....and it is true that there are many out there who should not be doing this job and are rather inappropiate in doing it.
But this is so with everything in life. There are people who are unable or disqualified in doing something but out of nothing else than their personal interest, they go on with it.
As in every profession, job or occupation, there are good examples and bad examples.
In case though someone is in need of a therapist either because of psychopathological reasons or simpler day life matters, he/she should not hesitate in investing some time into finding the one therapist that suits them the most.
A supportive, analytical process, which focuses on the present and practical issues can be Life Altering. It can enhance the way we live our lives and when surrounded by people in our immediate environments who need our help and support, we would have the means to provide it.
.
Lots of people say: "..but I'm not crazy (wrong choice of word in the first place)...not the one who needs a therapist...he/she is!"...well, my dear all, when we live with such people their issues become ours...and it is in the hands of the healthier and stronger to do something.
Yes, there is tremendous ammount of pain involved....there can also be tremendous ammount of relief and pleasure involved, too. It is a matter of choice.
And last but not least....no therapy will do a thing, unless it's done with the one and only intangible quality in life, which has the most tangible of effects on our lives: LOVE
If you've managed to read all this, then thank you from the bottom of my heart for having taken the time.
The loveliest of days to you all!
Ivy xx
Umm where do I start, at the beginning I suppose ;-)
For the last two weeks I have been making very discrete enquiries, and having many conversations with the owner of Peelings Coaches, about the prospect of the SWPG (well me!), having one of their coaches which they were due to scrap, and look into it possible preservation.
Thank goodness we still have some lovely family run companies, whose vehicles still mean something to them and the thought of seeing their member of the family scrapped would haunt them forever more. Well that is what was going to happen with UGB even though she still has 10 months MOT on her.
After lengthy and protracted negotiations, we were eventually told yesterday that she was ready to be collected from Tittleshall in Norfolk (Between Kings Lynn and Norwich). Johnathan Peeling even taxed the coach for 6 months and put 100 litres of fuel in it, a jesture that has been noted and won’t go unrewarded. SO after another 4.30am start and another trip on the 06.01 to London from Bristol Parkway, another tube journey on the Cirlce Line and another journey from “The Cross”, we eventually arrived in Norfolk at 11.00am.
The journey back to Bristol took 6 hours, with 4 stops and not wanting to rant her I sat at about 57/8 most of the way back, and traversed many local roads and A roads in Norfolk, before having our first break in Peterborough. We then took the A47, A605, A14, M6, M42 & M5 stopping at Corley and Strensham, before arriving back in the yard for 7pm.
SO why did I want another coach after getting rid of the Tiger a lot of you will ask, and some of you have that right. Well quite simply I have missed having a coach due t its comfort, and I think a group of our size needs it.
A652 UDG (Plaxton paramount 3500 bodied Volvo B10M) started out life with Park’s of Hamilton, in their gaudy Blue, White and Orange livery with the Trafalgar Tours logos attached to the side, before a few years with West Coast Motors in North Scotland. She was then sold to C J Down in Mary Tavy (Devon) where she spent quite a long time before being sold to a dealer in Leicestershire who sold her to Fowlers of Holbeach (Another coach in the group that has been at Fowlers!), before being sold to the Wonderful Peelings of Tittleshall, who have kept her rather immaculate. This coach has been stood for 2 months, and started on the button, and drove like a front line motor!
There are plans, but I won’t be shouting my mouth off about them, you will all just have to wait and see as I also have the Fleetline to get done (Which WILL NEVER BE SOLD!!!!!) ;-).
LE COEUR AU VENTRE
EXTENDED UNTIL 11 OCTOBER 2020
Art et Marges Museum: An outsider art museum, challenges art and its boundaries.
Passionate collectors, talent scouts and big hearted gallerists, Marion and L. Oster live amidst a fascinating torrent of outsider and expressionist art. This exhibition offers an unprecedented immersion into the world of these discrete collectors, by giving new life to this intriguing residence with a thousand inhabitants.
The art et marges musée museum contains a collection, compiled since the 1980s, outside the beaten tracks of the art world, among self-taught artists, art studios for persons with a mental disability or from psychiatric institutions.
The art et marges musée museum mounts exhibitions featuring artists from both sides of the margin.
The art et marges musée museum falls under what is known as outsider art
with a in situ artwork by Caroline Dahyot, and works by A.C.M, Abadne, Adam Sabhan, Aïni Philippe, Albasser Pierre, Amar Paul, Amourette Pierre, Angkasapura Noviadi, Armstrong Zebedee, Avril Armand, Azema Philippe, Babahoum, Badia, Barbarit Béatrice, Barbe-Hatuel Nicole, Barrameda, Baudelere Karl, Bauman Manuel, Beaver Larry, Ben Ali, Berquin Patricia, Birobent Martine, Blot Olivier, Bosco Giovanni, Branciard Jean, Brunet Guy, Burland Francois, Cadoré Delphine, Cahoreau Gustave, Cerredo Fabian, Chanut Danielle-Marie, Chauvet François, Chomette Virginie, Cluzel Nicolas, Comte Robin, Cooper Ronald, Corentin Sylvain, Cumingham Richard, D'antuono Barbara, Dahyot Caroline, De Sagazan Olivier, Dellschau Charles, Demelis Eric, Dereux Philippe, Dominici Véronique, Doñate Pepe, Doué Eric, Dubréus Lhérisson, Duclos Hélène, Dugnoille Myla, Duprilot Hubert, El Syrio Josvedi, Fillaudeau Noël, Finster Howard, Fleury Yves-Jules, Gallieni Jill, Gillet Lionel, Glamocak Zlatko, Golz Michael, Gordon Ted, Gougelin Eric, Goulet Marie-Thérèse, Goux Claudine, Greiner Thierry, Grunenwaldt Martha, Hinojosa Aaron, Hofer Josef, Jaber, Jacqui Danielle, Jagiello George, Jorgensen Hans, Joss, Kapela Paulo, Knopf Solange, Kumar Pradeep, La Pinturitas, Labrie Karine, Lacoste Alain, Lagnieu Hélène, Lambert Thierry, Laure Isabelle, Laurent Henri, Le Carré-Galimard Simone, Lefèvre Pierre, Liberman Cirléne, Lippstreu Alexis, Manca Bonaria, Marie Florence, Mariette, Margot Margot, Marshall Francis, Marte Daldo, Mecalco David, Michaels Damian, Mister Imagination, Monchatre François, Mond Mina, Montpied Bruno, Morel Marie, Mouly Gaston, Mustafa, Nadau Jean-Pierre, Nedjar Michel, Nitkowski Stani, Obata Masao, Oster Marion, Palmer Andrei, Park Chong-Ran, Patba58, Pelligand Bernard, Philippi Jean-Christophe, Pietquin Dimitri, Pietri Josselin, Pignat Armande, Plaza Amadeo, Plny Lubos, Podesta Giovanni Battista, Postic Evelyne, Raâk, Rae Helen, Rieux Jean-Francois, Rigal Antoine, Robert Yvonne, Robertson Royal, Robillard André, Rosset Jean, Saban Ody, Sablon Françoise, Sanders Jim, Schwanse Petra, Sendrey Gérard, Sesow Matt, Sharlhorne Welmon, St John Christopher, Staelens Ghyslaine Et Sylvain, Stroff Denis, Tanjung Ni, Tirilly Jean, Tourlonias Jean, Ughetto Henri, Ursin Catherine, Valois Marie-Françoise, Van Acker Jacqueline, Vigneau Monique, Vinsard Marcel, Vladimir, Webster Dereck, Wilson Ben, Zanon Juliette.
On the first floor, discover a selection of works from the museum's permanent collection, with: Inès Andouche, Jan Bedinsky, Georges Cauchy, Aloïse Corbaz, François De Jonge, Isabelle Denayer, Johan Geenens, Madge Gill, Martha Grunenwaldt, David Houis, Anne N’Dayiziga, Jean-Marie Mortier, André Prues, Nouzha Serroukh, Anny Servais, Jacques Trovic, André Wostijn.
Featured on my Blog at www.brusselspictures.com
French postcard by Editions O.P., Paris, no. 115. Photo: Teddy Piaz.
Discretely beautiful and charming Simone Valère (1923-2010) was primarily a famous French stage actress, but she also appeared in more than forty films from 1941 to 1993. She often worked together with her husband, Jean Desailly.
Simone Valère was born Simone Jeannine Gondolf in 1923 in Paris, France. Her parents divorced and she spent a large part of her youth with an aunt in Arnouville. At the age of 17, she made her first film appearance in Premier rendez-vous/Her First Affair (Henri Decoin, 1941) starring Daniëlle Darrieux. In 1942, Simone made her stage debut at the théâtre Hébertot in Paris in the play 'Mademoiselle Bourrat'. The play is situated in a village called 'Valère and she takes this as her stage name. Simone Valère met Jean Desailly on the set of the film Le Voyageur de la Toussaint (Louis Daquin, 1943), while he was working for the Comédie-Française and married to Nicole Desailly (pseudonym of Ginette Nicolas). They started to live together in 1950 on tour in Brazil. 48 years later, they married in Paris.
Simone Valère and Jean Desailly participated in the theatrical revival of the post-war period as part of the Renaud-Barrault company. There she performed in plays by Shakespeare, Kafka, Marivaux, Giraudoux, Molière, Ionesco, and she starred in the operetta 'Vie Parisien' by Offenbach. Later she and Desailly founded the company Valère-Desailly. With Madeleine Renaud and Jean-Louis Barrault, they were one of the most famous couples in French theatre. Simone Valère and Jean Desailly performed 450 times their favorite play, 'L'Amour fou ou la first surprise', by André Roussin. Valère also worked for the cinema in such films as La revanche de Roger la Honte/The Revenge of Roger (André Cayatte, 1946), and Violetas imperiales/Imperial violets (Richard Pottier, 1952) with Luis Mariano and Carmen Sevilla. She played the princess in the Faust adaptation La Beauté du diable/Beauty of the Devil (René Clair, 1950) with Gérard Philipe and Michel Simon. Other highlights were Le Franciscain de Bourges/Franciscan of Bourges (Claude Autant-Lara, 1968), starring Hardy Krüger, and L'Assassinat de Trotsky/The Assassination of Trotsky (Joseph Losey, 1972) starring Richard Burton and Alain Delon. Her last film was She made her last screen appearance in Équipe de nuit/Night Shift (Claude d'Anna, 1988. She was married to Jean Desailly till his death in 2008. Simone Valère died in 2010 in Roinville-sous-Dourdan, Essonne, France. She was 87.
Sources: Wikipedia (English and French) and IMDb.
And, please check out our blog European Film Star Postcards.
A five-dimensional space is a space with five dimensions. If interpreted physically, that is one more than the usual three spatial dimensions and the fourth dimension of time used in relativistic physics. It is an abstraction which occurs frequently in mathematics, where it is a legitimate construct. In physics and mathematics, a sequence of N numbers can be understood to represent a location in an N-dimensional space. Whether or not the universe is five-dimensional is a topic of debate.Three Logical Proofs: The Five-Dimensional Reality of Space-Time
West Virginia University at Parkersburg Physics, 300 Campus Drive Parkersburg, West Virginia 26104 e-mail: jebcolst@aol.com
Abstract- A century and a half ago, a revolution in human thought began that has gone largely unrecognized by modern scholars: A system of non-Euclidean geometries was developed that literally changed the way that we view our world. At first, some thought that space itself was non-Euclidean and four-dimensional, but Einstein ended that 'speculation' when he declared that time was the fourth dimension. Yet our commonly perceived space is four-dimensional. Einstein unwittingly circumvented that particular revolution in thought and delayed its completion for a later day, although his work was also necessary for the completion of that revolution. That later day is now approaching. The natural progress of science has brought us back to the point where science again needs to consider the physical reality of a higher-dimensional space. Science must acknowledge the truth that space is four-dimensional and space-time is five- dimensional, as required by accepted physical theories and observations, before it can move forward with a new unified fundamental theory of physical reality.
Keywords: four-dimensional-five-dimensional-space-time-Einstein- Clifford- Kaluza- Kaluza-Klein- magnetic vector potential- electromagnetism- Yukawa potential- xpanding universe- general relativity-unification-superstrings-branes-Randall-Sundmm
Introduction
Individual scientists have been searching for evidence of a fourth dimension of space for more than a century and a half. That search subsided somewhat after Albert Einstein identified time as the fourth dimension and developed the theories of relativity. However, Theodor Kaluza added a fifth dimension to space-time in 1921. Others have contributed to this line of scientific devel- opment, but not to as high an extent. Given the fact the physicists have now developed 10- and 11-dimensional theories of reality, it would seem that the search for a fourth dimension of space would have taken on a new and sig- nificant meaning, but it has not. Yet several generally accepted scientific theories and concepts do imply the existence of a fourth spatial dimension.
On the other hand, a growing number of scientists have acknowledged and embraced the simple fact that physics needs a single fundamental theory to
524 J. E. Beichler
continue its astonishing rate of progress. A complete unification of the funda- mental forces of nature has itself been a long process predating the 1970s, but that unification was made basically from the relativistic point-of-view by Einstein and a few other scientists before the 1960s. Einstein searched for a successful unification of gravity and electromagnetism for the last three decades of his life, hoping that the quantum and quantum effects would emerge from the mathematical formalisms of his unified field theory, but most other scientists shared neither his optimism nor his goal. During the 1970s, quantum physicists finally adopted Einstein's goal, but not his emphasis on a unification based upon general relativity and a continuous view of the ultimate nature of reality. Quantum theorists began their own long search for unification with the discovery of the standard model, then the electroweak force and finally the hope that gravity would eventually submit to quantum analysis. They have utterly failed to achieve this last step toward unification.
All that science can say for certain is that there are presently two theories that can claim to represent the most fundamental nature of reality: Quantum theory and relativity. Unfortunately, these two are mutually incompatible. The near complete dominance of the quantum paradigm over the last century has led most physicists to conclude that any future theory that unifies physics must be based upon a discrete quantum model rather than a continuous relativistic model. The attitude that discreteness can replace continuity at all levels of reality is prob- lematic: It reflects a general disregard for the depth and extreme nature of the major differences between the two theories. This disregard has led scientists to speculate on the structure of reality at as small a level as the Planck length, resulting in the development of quantum loop theories and other attempts to find a quantum gravity theory. Whether the existence of a major conflict between the discrete and continuous is acknowledged or not, the fact that these two models of reality are mutually incompatible is generally minimized or belittled by many theoretical scientists who overwhelmingly assume that discreteness offers the only possible solution to the problem of unification.
Recent attempts to overcome this incompatibility, such as the supergravity, superstring and brane theories, have relied heavily upon the concept of hyper- dimensional spaces. These models have been unsuccessful, yet the overall notion of hyper-dimensionality still offers a way out of the dilemma. Einstein first rendered the notion of a higher-dimensional reality plausible in 1905, but the revolution that Einstein began when he unified three-dimensional space with time to form a four-dimensional space-time continuum has never been fully realized. In the meantime, the opposing quantum concept may have fully run its course and reached its inherent theoretical limits. The modem unification theories based upon the quantum model do not seek to rectify the fundamental differences between the quantum theory and special relativity. Quantum field theories only calculate quantum effects in the relativistic limit; they do not unify the theories at the necessary fundamental level that is often claimed. Many scientists ignore the extent and importance of the differences between continuity
Five Dimensions of Space-Time 525
and the discrete and instead worry about the insignificant problems of inde- terminism and counting bits of information. So the latest attempts at unification have failed utterly even though the quantum theory has been attempting to quantize gravity for several decades.
There are many levels to the hyper-dimensionality problem, many of which have not yet been explored even though the central problem of dimensionality for present day science dates back a century and a half. Science has been misled and has failed to recognize the significance of a far more fundamental revolution that began in the 1850s when Bernhard Riemann developed a generalized system of non-Euclidean geometries (Riemann, 1854). Riemann's work directly implied that space is four-dimensional as well as continuous. His new system of geometry remained relatively unknown for more than a decade and was only popularized within the scientific community in the late 1860s. Simultaneously, James Clerk Maxwell developed Michael Faraday's field concept of electro- magnetism into a complete theory of electromagnetism. Whether the timing of these developments was coincidental or not, and only a careful review of historical documents can determine if the simultaneous development of these theories was truly a coincidence, the two fundamental concepts of the continuity of the electromagnetic field and the four-dimensionality of space are physically related. There are three logical proofs that this fact is true.
The first logical proof derives directly from Maxwell's electromagnetic theory and deals directly with the inability of science to sufficiently explain the nature of the vector or magnetic potential used to explain magnetic induction. The second logical proof deals with the nature of matter itself as represented by the Yukawa potential and the atomic nucleus. The Yukawa potential is normally used to explain how electrical repulsion is overcome to bind particles within the nucleus. However, the mathematical expression for the potential also matches the general shape of space-time curvature within the individual particles that combine to form the nucleus. And finally, the last proof is a more general argu- ment dealing with the simple three-dimensional orientations of spiral galaxies relative to the Riemannian curvature of the universe as a whole. Although these proofs are independent of any particular modern hyper-dimensional theory, they are supported by Kaluza's theory of five-dimensional space-time.
Electromagnetism Speaks Up
The popular concept of a 'force field' is completely erroneous. Even in a classical sense, no force is associated with a field until a material particle or body interacts with it. Force is not a characteristic of the field alone. The interaction of the field and matter results in the force, but the interaction can also be characterized by a potential energy. The energy results from the force acting on the particle in one sense, or from the relative position of the particle in the field in another sense. What exists at any particular position in the field before the interaction takes place is called the potential. So a physical field is char- acterized by the potential of the field, not a force.
526 J. E. Beichler
Gravity presents a good example for the concept of potential. Gravitational field strength decreases radially outward from the center of gravity of a material body like the earth according to the inverse square law. All points that are equidistant from the center of gravity form a surface in three-dimensional space along which the gravitational potential is constant, an equipotential surface. At each point on this surface, the surface is perpendicular to a radial line drawn from the center of gravity. A material body orbiting the earth would have a constant speed along any equipotential surface. Electricity presents another simple example. In this case, the units of potential are 'volts', a common electrical unit with which everyone is familiar. Equipotential surfaces representing specific volt measurements are a commonly accepted fact of electrical fields. The fact that an equipotential surface can be formed and that the surface is perpendicular to the radius of curvature at each and every point where they intersect is a general property of fields. From a theoretical point-of-view, equipotential surfaces must exist for all physical fields. For any field, successive equipotential surfaces form onionskin-like concentric surfaces around point charges or charged bodies.
There is a direct equivalence between electricity and magnetism and that equivalence forms the basis of the electromagnetic theory. Any physical quan- tities or properties of electricity correspond to similar quantities and properties for magnetism. But that equivalence has not yet been fully realized since there is no such thing as magnetic 'volts' or measurable magnetic potential. Magnetic potential has been, is now and will be in the future a mathematical entity alone, given the three-dimensionality of space. Consider a simple magnetic field, per- haps that of a bar magnetic. An equipotential surface cannot be drawn or represented visually as it can for an electric field, although magnetic field lines can still represent the field. A line perpendicular to any field line through a given point on that field line, representing the magnetic vector potential at that point, cannot be connected to neighboring points of equal potential on other field lines to form a continuous surface. In other words, an equipotential surface cannot be formed in the three-dimensional space of the magnetic field represented by the field lines. All equipotential surfaces would go through the same point on a field line in three-dimensional space, which is impossible, but no other conclusion can be reached from the given physical geometry of the magnetic field.
According to Roger Penrose, the magnetic potential is "not uniquely determined by the field F, but is fixed to within the addition of a quantity dO where O is some real scalar field." The scalar field is taken to be a purely mathematical entity, such that the magnetic potential A "is not a locally mea- surable quantity" (Penrose, 2005).The magnetic potential A exists, but no phys- ical experiment can measure or otherwise determine the value of A plus the additional quantity dO, so the value of A alone cannot be uniquely determined. In a sense then, the magnetic potential exists only at the point of intersection, not beyond that point in three-dimensional space. Magnetic potential is purely a point phenomenon in three-dimensional space no matter what its value. It is a mathematical paradox, but the paradox can be solved if a higher dimension to
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space is used. Any connection between a given potential on one field line and neighboring field lines must be in another dimension (orthogonal direction) other than the three normal directions of common space, in order for there to exist an equipotential surface. The 'gauge factor' dO mentioned by Penrose actually represents a minuscule measurement or perturbation in the fourth direction that does not otherwise affect normal three-dimensional field variations in the local environment. This fact can also be seen in the equations that are commonly used to express and model magnetic potential.
Although it cannot be described or measured in a normal three-dimensional space, the magnetic potential can be expressed mathematically, by its rela- tionship to the field, as
and
where B is the magnetic field strength. In this form, the quantity A is known as the magnetic vector potential or just the vector potential. Since the operator
V= (dldxi,dldyj,d/dzk),
taking the curl of A would be the mathematical equivalent of constructing the magnetic field B point-by-point by simultaneously looking at the perpendicular components to A in each of the three dimensions of space. These equations may seem trivial to physicists, but they have far more physical meaning than they have been given in the normally accepted electromagnetic interpretation.
The potential A must be simultaneously perpendicular to all three coordinates used to represent a point in space according to these formulations. However, the only 'thing' that can be perpendicular to all three dimensions of space simulta- neously would be a fourth orthogonal dimension. Therefore, changes in the magnetic potential as well as magnetic potential itself are perpendicular to all three directions at any spatial position in our normally perceived physical space. Different equipotential surfaces would still be expressed by three-dimensional equations even though they are displaced in the fourth direction because they would act like three-dimensional spaces that are parallel to or stacked on top of our common three-dimensional space in the fourth direction. Given the con- tinuity of space, our three-dimensional material world is actually embedded in a four-dimensional space (or manifold). Bernhard Riemann's original develop- ment of the generalized formulations of non-Euclidean geometry posited that an n-dimensional space would be embedded in an n+l-dimensional manifold, which implies that the physical reality of our three-dimensional space (where n= 3) requires the existence of a higher-dimensional manifold. In present theories of higher-dimensional spaces, such as the various superstring theories, several higher embedding dimensions are used, but the Riemannian mathematics used in general relativity only 'requires' one higher embedding dimension.
528 J. E. Beichler
The fact that magnetism implies a fourth dimension is not new. William Kingdom Clifford, a British geometer, tried to express Maxwell's electromag- netic theory using a four-dimensional space model in the 1870s. Clifford is better known for offering the first translation of Riemann's Habilitationsschrift lecture, " On the hypotheses which lie at the bases of geometry" , into English in 1873, among other things. Based on his understanding and interpretation of Riemann's geometry, Clifford claimed that what we sense as matter is nothing more than three-dimensional space curved in a fourth dimension and what we conceive as matter in motion is no more than variations in that curvature (Clifford, 1870). For having stated this, Clifford's geometrical model of space is normally regarded as a precursor to Einstein's model of space-time curvature in the general theory of relativity. Most twentieth century scholars have also concluded that Clifford never developed a theory and had no followers (Eddington, 1921; d'Abro, 1927; Bell, 1940; Jammer, 1954; Hoffman, 1972; Kilmister, 1973; Swenson, 1979)' so his theoretical work is viewed in this regard as a historical footnote and no more. The mathematician and historian E.T. Bell has gone so far as to characterized Clifford's anticipation of Einstein as little more than a case of some lucky person hitting "the side of a barn at forty yards with a charge of buckshot" (Bell, 1937), but this view of history is completely false. While Clifford's physical theories have gone unnoticed, Clifford numbers and his system of bi-quaternions have found new uses in some modern interpretations of quantum theory and relativity (Power, 1970; Gurney, 1983; Chisholm and Common, 1985) even though they were originally developed to describe his four-dimensional space, a fact that should imply new ways of interpreting the quantum.
Many modern scholars have mistakenly interpreted Clifford's theoretical model of a four-dimensional space in physics against a historical mindset biased by an early twentieth century view of general relativity (Beichler, 1996). Clifford's main purpose was not to develop a new theory of gravity, as did Einstein several decades later. Clifford's original theoretical work only dealt with Maxwell's electromagnetic theory even though he planned to add gravity to his theory at a later date (Clifford, 1887), if he had not died. Actually, Clifford was developing what we would today consider a unified field theory or better yet a theory of everything. He was fond of saying that he was " solving the universe" (Pollock in Clifford, 1879),which was his way of describing a single theory that covered all of the natural forces. Clifford attempted first to explain magnetic induction, not gravity, with his four-dimensional geometry (Pearson in Clifford, 1885). Magnetic induction is governed by the equation B = V@A, providing a direct link between the current logical argument for a four-dimensional space and Clifford's interpretation of Maxwell's electromagnetic induction.
Clifford published numerous mathematical papers on the motion of three- dimensional matter in four-dimensional elliptical (single polar Riemannian) spaces. He also published a book that actually presented his first step in building a proper theory, that is, for any of his peers who understood what he was trying to do. Historians and scholars today do not understand what Clifford was
Five Dimensions of Space-Time 529
attempting to accomplish, so they only see the book as a simple introductory trea- tise on kinematics. Anyone looking for a completed gravity theory in Clifford's work simply will not find it. Nearly all modern historians have mistakenly claimed that he never published his theory because they are looking for a nonexistent gravity theory with time as a fourth dimension.
Clifford expressed the opinion that all energies are either potential or kinetic (Clifford, 1880), but he also believed that kinetic energies in three-dimensional space would become potential energies in his four-dimensional spatial frame- work. In other words, forces in three-dimensional space would reduce to constant variations in position along paths in a four-dimensional curved space, an idea that was made current in general relativity. However, the modern concept only deals with gravity as modeled by modem relativity theory while Clifford meant to apply the concept to all forces in his model. Upon this hypothesis, he published the first volume of a series of books titled Elements of Dynamic (Clifford, 1878). His first volume was subtitled Kinematics. Everyone that knew Clifford or his work knew that dynamics in three-dimensional space is just kinematics in Clifford's four-dimensional space, that is why he referred to his explanation of Dynamics as Kinematics in the book title. He was writing about four-dimensional kinematics, which was equivalent to three-dimensional dynamics in his mind and theoretical model. Coincidentally, this same book is recognized by historians as the first published statement by a mathematician that distinguished between the cross and dot products in vector algebra (Crowe, 1967), the same dot and cross products that are used in the vector and scalar representations of magnetic potential given above. It should be clear then that Clifford understood the four- dimensionality of magnetic potential a full century before the modem scientific community took the unification of gravity and electromagnetism seriously.
In developing his theory, Clifford faced the problem that no mathematical formalism existed to express his four-dimensional ideas. So he used a form of quaternions of his own invention (bi-quaternions) to express his four- dimensional model of space (Clifford, 1882). Unfortunately, quaternions lost favor in the late nineteenth century to vectors and their use was largely aban- doned during the first few decades of the twentieth century. So no one today would even recognize that Clifford's mathematics represented his four- dimensional theory of physical reality. Einstein's theoretical work on a theory of gravity used the Levi-Civita tensor formalisms that had developed along a different line of reasoning than Clifford used for his quaternion algebra. The tensor calculus used by Einstein was only developed after Clifford's death.
As stated above, Clifford did not ignore the effect of his four-dimensional model of matter on the Newtonian theory of gravity. Clifford died of consumption in 1879 at the age of 34 and never completed his research, but it is still possible to discover what he planned to eventually accomplish with his four-dimensional model. His colleagues were so impressed with his theoretical ideas that both his published and unpublished works were collected, edited and published within a decade after his death. His followers and colleagues
530 J. E. Beichler
published everything that they could find, including lecture notes of classes that he taught, because they thought that his theoretical work was important enough to save for posterity and the future. Clifford's outline for the second volume of his Elements of Dynamic was among the unfinished works that were published. His student Robert Tucker edited this book. In it, Clifford stated his views on the theory of gravity and outlined how he would change gravity given his new four- dimensional geometry, thus indicating the fact that he was searching for, and may have found but never published, a unified field theory. But we will never know that fact for sure.
Of course, philosophical and mathematical arguments are not as valuable in science as observation and experimental verification. Yet there is some experi- mental evidence supporting the existence of magnetic potential in the Aharonov- Bohm effect (Aharonov & Bohm, 1959). In the Aharonov-Bohm experiment, an electron beam is split in such a manner that the two resulting beams pass on either side of an upright solenoid before coming back together on a screen. The solenoid is oriented in such a way that the twin beams cut across the field lines (perpendicular to B) and thus the net force acting on them is zero. Yet when the beams come together at the screen they interfere with each other. The interference clearly shows that the wave functions associated with the electron beams are out of phase, yet they should not be out of phase by the normal standards of Maxwell's electromagnetic theory. Although the effect is somewhat paradoxical, it is normally interpreted as evidence that the magnetic potential associated with the magnetic field is real even though it cannot be measured or experimentally determined. While the net force is zero, an integration of the potential A in a closed loop around the coil is not zero. The common interpretation of this experiment introduces a quantum solution (Bohm & Hiley, 1993). However, this effect can be simply explained and understood within the four-dimensional framework of electromagnetic induction. In other words, a classical electromagnetic interpretation can be used to explain the results if a physically real four-dimensional space that is associated with the magnetic vector potential is assumed.
While the net force is zero on either of the electron beams, the electrons are moving at a constant speed through different portions of the coil's mag- netic field. So they each follow paths of varying potential (surfaces) in four- dimensional space corresponding to the portions of the magnetic field through which they travel. Since they are following four-dimensional paths of different lengths, they are out of phase when they reach the screen and interfere with each other. The principle is similar to a satellite orbiting the earth at a constant speed. The constant speed holds the satellite to a path along a gravitational equi- potential surface. When the speed changes, the satellite follows a path through different equipotential surfaces. The orbital speed determines the altitude of the orbit and the potential path (surface) along which the satellite travels. The electrons in the beam also follow curved potential paths in the fourth dimension, which are different according to the portions of the magnetic field through which
Five Dimensions of Space-Time 531
they pass in three-dimensional space. The difference in curved paths in four- dimensional space puts them out of phase at the end of the trip even though their paths in three-dimensional space, the projections of their paths in four- dimensional space, are not curved.
And finally, given a real fourth dimension of space that is characterized by magnetic potential, anything that emits a normal transverse electromagnetic wave in three-dimensional space would also cause a corresponding compressive wave of magnetic potential variation in the fourth direction of space. Numerous scientists have claimed to show the mathematical possibility of such longitudinal electromagnetic waves. Edmund T. Whittaker's model of 1903 is perhaps the best known of these attempts (Whittaker 1903, 1904). According to Whittaker,
... thus we have the result, that the general solution of Laplace's equation
wheref is an arbitrary function of the two arguments z+ix cos u+iy sin u and u.
Moreover, it is clear from the proof that no generality is lost by supposing thatf is a periodic function of u (Whittaker, 1903).
The variable u actually represents the fourth dimension of space while V is the magnetic potential. This interpretation renders Whittaker's formulation com- patible with modem advances in the laws of electromagnetism without surren- dering the possibility of a longitudinal electromagnetic wave. The function f is periodical with respect to u, which means that the fourth dimension is closed with respect to the other three dimensions of space. This closure corresponds completely to Kaluza's closure condition for the fifth dimension of space-time, while the factor of du over which the function f is integrated corresponds to Penrose's gauge invariance dO.
In this respect, the fourth dimension of space is independent of the length of the extension in the fourth direction, such that the fifth direction of space-time can be either microscopic or macroscopic in extent. There is no difference between the two in the functionf as long as the fourth dimension of space is closed. Whittaker then analyzed the general form of the differential equations for wave motion
to demonstrate that the mathematical model can account for a longitudinal
532 J. E. Beichler
electromagnetic wave. However, if V is taken to mean the magnetic potential in the fourth direction of space, then the magnetic potential V can be related directly to the concept of proper time in special relativity. Whittaker's concept
I of a longitudinal component of electromagnetic waves can thus be rendered
~
in relativistic terms, which implies that the concept is actually a wave of changing magnetic potential propagating in the fifth direction of a five- dimensional space-time continuum.
Whether or not Maxwell's electromagnetic theory requires a longitudinal wave in its classical three-dimensional interpretation is open to debate, but the existence of a fourth dimension to space would require a corresponding longi- tudinal wave that propagates throughout the fourth dimension relative to the normal three dimensions of space. No one has ever detected a three-dimensional longitudinal wave, but that does not mean the wave cannot be four-dimensional. After all, no one has ever detected or measured a 'magnetic-volt' of potential in three-dimensional space either, even though the potential exists in four- dimensional space.
The Yukawa Field
Modern physics also requires the existence of a fourth spatial dimension, but this time the culprit is the Yukawa potential. The Yukawa potential normally takes the form
The quantity g is real. It represents the coupling constant between the meson field and the fermion with which it interacts, at least in the normal quantum interpretation. The Yukawa potential itself arises from the exchange of a massive scalar field or particle such as the pi meson or pion (Yukawa, 1935). The nega- tive sign guarantees that the force between particles in the nucleus is always attractive.
This potential is associated with the extremely short-range strong nuclear force and it is usually only interpreted as a quantum phenomenon. The potential associated with the Yukawa field decreases exponentially, guaranteeing the short range of the Yukawa field to little more than the outer boundaries of the nucleus. It is simply assumed that the Yukawa field cannot be interpreted within a non-quantum context, yet there is no hard and fast rule that states that the Yukawa potential cannot be interpreted geometrically. Classical fields are nor- mally interpreted geometrically, so it would seem that the Yukawa field should also have a geometrical interpretation. Even the modern view of gravity as resulting from the curvature of space-time is geometrical in nature.
According to a simple interpretation of physical laws, the field strengths of both electric and gravitational fields vary as llr2. Traditionally, this inverse square law has been interpreted as resulting from the three-dimensionality of
Five Dimensions of Space-Time 533
this may seem, the inverse square law has been used in the past to explain the necessity of a three-dimensional space to the laws of physics (Whitrow, 1955; Abramenko, 1958; Biichel, 1963; Freeman, 1969). In other words, the inverse square law is normally thought to imply (if not prove) that space 'must be' three-dimensional. It has also been a common practice in the past to criticize higher-dimensional theories by pointing out that gravity would not work in a higher-dimensioned space because the inverse square law would not apply. However, we commonly accept the notion of a four-dimensional space-time without any alteration to the inverse square law without realizing that we do so. The fourth dimension of time is both qualitatively and quantitatively different from the normal three dimensions of space, so it does not affect the inverse square law. By the same token, there is no hard and fast rule that unequivocally requires that a fourth dimension of space would be both quantitatively and qualitatively the same as our normal three dimensions of space. In fact, given the reality of a fourth dimension of space, nature seems to have ordained that the fourth dimension is different from our normal three dimensions of space and nature rules physics instead of the other way around. So there is no valid or compelling reason to assume that a fourth spatial dimension would have any effect on the inverse square law and gravity. In fact there are reasons to believe that the opposite is true.
Many scientists have long believed that matter is electrically constituted and electricity acts according to the inverse square law. Our perception of space is dependent on the relative positions of matter in that space. So if matter is three- dimensional we sense space as three-dimensional. The three-dimensional surface curvature of a material particle or material body may be sufficient to determine the three-dimensionality of space, but the complete three- dimensionality of the particle is not necessary according to how it outwardly appears. Nor is it complete. The interior portion of a material particle could still be higher dimensional. For instance, the interior of a proton could be a physical singularity stretching into a higher fourth dimension even though the exterior surface of the proton is still curved spherically in three-dimensional space. Space
1 could have any number of dimensions while three-dimensional matter only determines that part of the space or manifold in which the electrical field acts and reacts. Our normal senses evolved in the three-dimensional material world of nature, so they would be limited to detect only the three-dimensionality of matter even given a real fourth dimension. Since gravity acts between material particles, which are three-dimensional due to their electrical nature, it would also act three-dimensionally even if space had four or more dimensions. While it is commonly argued that space is three-dimensional because of the inverse square law, it could also be argued that we only sense three out of a greater number of dimensions because of the inverse square law by which gravity and electricity act as they do in three dimensions.
It seems that the inverse square law only guarantees the three-dimensional actions and interactions of matter, not the other way around. The forces
534 J. E. Beichler
associated with common fields act three-dimensionally and no more. The inverse square law does not guarantee that either space itself or fields in general are three-dimensional or otherwise limited to three dimensions. Fields could be higher-dimensional entities just as space could be higher dimensional even though we only sense three dimensions of space. Matter reacts with fields in three- dimensional space because matter is outwardly three-dimensional, not because fields are three-dimensional. If fields are higher dimensional, there may be field- field interactions that occur only in the higher dimensions of space and thus remain undetected in the three-dimensional material space except by their sec- ondary effects. An effect such as quantum entanglement could be explained in this manner. When all is taken into account, neither physical fields nor space need be limited to three dimensions by either the laws of nature or logic and reason.
On the other hand, the potentials associated with fields vary as llr. So
a physical field associated with a particular potential has one more factor of the
2
variable 'r' than the potential itself because fields vary as l/r . The dimen-
sionality of the space that the field occupies is generally two greater than the exponent of the variable 'r' in the denominator of the formula representing the potential. This logic also follows for the Yukawa potential: The variable 'r' in the denominator reflects the three-dimensionality of the field, but there is another term with an 'r-' factor in the exponent in the numerator of the formula. The variable 'r' in the numerator of the formula could easily represent another dimension, so the Yukawa potential would require that the space occupied by the Yukawa field is four-dimensional, not three-dimensional. The exponential term eKkrrepresents both the geometrical structure of the particle and its associated field as extended into the fourth dimension of space. The extension of a particle in the fourth direction would occur internally relative to three-dimensional space so that the part of the material particle that we sense or detect remains the three- dimensional exterior surface of the particle.
In this model of the Yukawa potential and field, the variable 'r' in the denominator would account for the spherical shape of elementary particles and the nucleus itself. By analogy, this would indicate that the exponential term in the numerator would refer to the geometrical shape of the Yukawa field in the higher fourth dimension. If the Yukawa field conforms to the shape of an exponential curve in the higher dimension, as opposed to the spherical shape in three-dimensional space, then the fourth dimension of space is most certainly different from the other three dimensions of normal space, as noted above.
In fact, elementary particles such as protons and neutrons would be small singularities according to the general theory of relativity; or rather they would be singular at their centers. They would therefore follow curved space-time in a shape similar to a rotated exponential curve, as shown in a normal drawing of the curved metric of a singularity (see Figure 1).
So the Yukawa field would correspond to the shape of a nucleus or elementary particles predicted by relativity theory, if general relativity is taken to depict a real curvature of three-dimensional space in a higher embedding fourth
Five Dimensions of Space-Time 535
Exponential curves define the outer shape of the singularity in
Fig. 1. The internal curvature of an elementary particle.
dimension of space. At this point, there is no need to assume a dimensionality greater than four as used in some recent theories, although there are no re- strictions on space having more than four dimensions. Moreover, the curvature of space-time in general relativity is a function of the mass of a particle or body. The constant k in the Yukawa potential is also related to the mass of the exchange particle between nucleons. In both cases, the mass is related to the curvature explicit in the mathematical model, which indicates that the Yukawa potential could be modeled by the curvature of space-time as expressed by the theory of relativity rather than the particle exchange concept of quantum field theory. In either case, the Yukawa potential logically requires that space is four- dimensional and thus the space-time continuum of relativity is five-dimensional. The relationship between the Yukawa potential and general relativity leads to the third logical proof that space is four-dimensional, only this time the proof deals with the macroscopic world of the greater universe rather than the microscopic world of the quantum.
The Cosmological Connection
In the late 1920s, Edwin Hubble observed that other galaxies were receding from our Milky Way galaxy with increasing speed as the distance to the other galaxies increased. These observations indicated that our universe is expanding. Georges-Henri Lemaitre and others who developed the expansion hypothesis by a theoretical application of general relativity had already predicted the expansion. The marriage of observation and theory in this case produced one of the most spectacular successes for science in the twentieth century. The simple notion of an expanding universe is usually explained by analogy to a two- dimensional surface expanding in a third dimension.
A good example would be a balloon with spirals drawn on its surface to represent galaxies. When the balloon is blown up and expands, the spirals spread
536 J. E. Beichler
apart and move away from each other in the same pattern of motion that the receding galaxies show during astronomical observation. The expanding surface of the balloon is analogous to our expanding universe, the difference being that the balloon is a two-dimensional surface expanding outward in a third direction while the universe is a three-dimensional surface expanding into 'who knows what'. Although the phrase 'who knows what' is not an appropriate phrase for scientific use, it does represent how science views the question of what the universe is expanding into.
Some versions of modern brane theory postulate variously dimensioned branes curved in higher-dimensional bulks, so brane theorists could claim that the universe is expanding into the embedding bulks. However, brane theories have other problems to overcome: There is a discontinuity between the branes and the bulks in which they are embedded, such that the branes and bulks are separate things. As such, they break the continuity of the space-time continuum. The brane theories are based upon Klein's interpretation of Kaluza's five-dimensional theory of space-time, but they violate the basic assumptions upon which Kaluza unified electromagnetism and gravity as expressed by general relativity: Kaluza assumed the continuity of four-dimensional space-time with the fifth and higher dimension. So it would seem that the brane theories as well as the superstring theories upon which they were conslrucled are at odds with their own basic premise.
However, the balloon analogy gives more information about the expansion than ordinarily suspected, which implies an answer to this unanswered question about what the universe is expanding into. The spirals drawn on the balloon's surface are all rotating and expanding relative to a single point, the geometric center of the balloon, rather than any center on the surface of the balloon. This part of the analogy is often used to argue that our universe has no center within its three-dimensional expanse, which is true. The curvature of space-time in general relativity has always been considered an intrinsic property of space-time such that a higher embedding dimension has been unnecessary to explain observed and suspected phenomena. However, a higher embedding dimension, demonstrating that the curvature of space-time is an extrinsic property, is still perfectly compatible with general relativity (Misner et al., 1973). Extrinsic curvature is sufficient to explain the effects of general relativity, but has never been considered necessary as long as the idea of intrinsic curvature was con- sidered more likely. But if the concept of extrinsic curvature and a higher embedding spatial dimension does not represent our true reality, simple rela- tivity will be violated in the case of the expanding universe and other astronomical observations.
In the balloon analogy, as stated above, the plane of rotation of the spirals and the recession of the spirals as the balloon expands are all oriented relative to a single point, the center of curvature of the balloon's surface. In the real three-dimensional spatially extended universe, all of the galaxies rotate and recede from each other at all possible angles or orientations in three-dimensional space. Yet you cannot have a mathematical property true for one configuration
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of spatial dimensions (two dimensions embedded in three-dimensional space) that is not true for another configuration (three dimensions embedded in a four- dimensional space). Such an inconsistency would destroy the validity of the mathematical model. The general geometric properties are the same for all spaces and embedding manifolds for an n-dimensional geometry embedded in an n+l-dimensional manifold. Riemannian geometry is based upon this simple idea. So, there is a logical necessity that the orientation of all of the galaxies in the expanding universe be relative to a single point or center of curvature of the universe. The natural rotations of galaxies in the universe are all relative to the same point, and the planes of galactic rotation are all tangential to the three- dimensional surface that is our space, which is perpendicular to the real extrinsic radii drawn between them and the center of a physically real curvature of our universe in a fourth spatial dimension.
In this case, it is illogical to speak of the overall curvature of the universe and then deny the reality of the higher embedding dimension because of a human sensory and perceptual bias against the possibility of a fourth spatial dimension. Perhaps local spatial curvature can be explained away as an intrinsic charac- teristic of the space-time continuum, but the concept of intrinsic curvature on a global level is untenable. The notion of an intrinsic radius of curvature for the whole of the universe is illogical. The three-dimensional surface of our universe is closed such that it forms a Riemannian sphere, which would require a higher embedding dimension to account for the closure. Once again, the only way to derive a direction perpendicular to all three dimensions of space simultaneously would be to adopt the geometry of a real four-dimensional embedding space. That fourth dimension or direction is orthogonal to the normal three dimensions of space. So the observed three-dimensional orientation of astronomical bodies directly requires the reality of a fourth spatial dimension. In effect, our three- dimensional universe is expanding into a fourth dimension of space. The simple fundamental notions of relative motion and actual observation, rather than any specific theory, logically require that our space is four-dimensional and thus space-time is five-dimensional.
The Kaluza Confirmation
While these logical proofs may not be completely persuasive or even persuasive enough to sway the attitudes of many within the general scientific community, there are other extenuating factors and circumstances that should be persuasive given the validity of the logical proofs. Also, these three logical proofs should be considered independent of any particular hyper-dimensional theory of space-time. They only indicate that some higher-dimensional theory would give a more correct picture of our physical reality without specifying the exact theory to be used. Yet there is already a specific scientific theory that successfully utilizes a five-dimensional space-time geometry to unify general relativity and electromagnetism: Kaluza's 1921 theory. Kaluza's theory has been largely ignored in spite of its successful derivation of Maxwell's electromagnetic
538 J. E. Beichler
theory from the general relativity of a five-dimensional space-time continuum. Most modern scientists are only familiar with Kaluza's theory through its association with the work of Oskar Klein, altering the theory to the Kaluza-Klein model of space-time. Little is known of Kaluza's original theory under these circumstances. Klein's subsequent adaptation of the theory (Klein 1926a, 1926b, 1927) was an attempt to incorporate quantum theory into the geometry of space-
time. But Kaluza's theory can stand alone on its own merits, without considering 7
Klein s extended version of the theory into the realm of the quantum. Kaluza's original theory had nothing to do with the quantum.
According to Kaluza's original theory, two mathematical conditions are necessary to unify general relativity and electromagnetic theory. All points in the four-dimensional space-time continuum are extended orthogonally into the fifth dimension along what Kaluza called A-lines. The A-lines follow circular paths in the fifth direction back to our space-time continuum, so they are closed with respect to the fifth direction. Kaluza's first condition was to close the system in the fifth direction, but the A-lines were also required to be of equal length, giving the second condition. Kaluza also suggested that the A-lines are infinitesimally short to guarantee that we could not detect the fifth dimension, although this suggestion was not a required mathematical condition. The two conditions were necessary to guarantee the mathematical consequences of add- ing the fifth dimension: Deriving the equations of general relativity by applying a four-transformation while obtaining the equations of electromagnetism by applying a cut-transformation.
If either of the initial conditions were to be changed or relaxed in any manner, it is possible and even likely that the results of the change would render electromagnetism and gravity incompatible if not break Kaluza's link between them altogether. But Kaluza also assumed, without so stating, a third condition of continuity in the fifth direction. Continuity was built into the calculus that Kaluza used to develop his geometrical model. So if continuity is forfeited, then Kaluza's theory could still fall apart. Before any of these conditions is changed in new extensions of Kaluza's theory, it must be shown that any of these changes, or any combination of them, does not alter Kaluza's results, the unifi- cation of gravity and electromagnetism. There are no middle roads to take here; it is all either black or white. If Kaluza's initial conditions were altered in any manner that breaks or weakens the link between gravity and electromagnetism, then the extension would be invalid for having destroyed the very foundations upon which the new theory is based. Yet changes in these conditions have been made to expedite the development of modern theories and thus could have a direct bearing on the validity of the supergravity, superstring and brane theories, all of which depend on extended versions of the Kaluza-Klein model.
When Klein adopted Kaluza's theory in an attempt to quantize the unified field, he did not relax or alter Kaluza's conditions. He merely followed Kaluza's suggestion that the extension in the fifth direction must be extremely small since we cannot detect the extra dimension. Klein equated the periodicity in the
Five Dimensions of Space-Time 539
'closed loop' condition to the quantum of action. At the time, Klein's version of the theory was largely ignored by the scientific community, which was mesmer- ized by other developments in quantum theory such as quantum mechanics and wave mechanics. Unfortunately, Klein could not make his theory work. He rejected his first theory and made two later attempts to rectify the errors in his theory, in 1939 and 1947 (Klein 1939, 1947), but eventually rejected his basic hypothesis and gave his theory up as a lost cause.
Klein's adaptation of Kaluza's theory, the Kaluza-Klein theory, was re- discovered in the 1970s and adopted by supergravity theorists as a method to unify gravity with the latest versions of the quantum field theories and the standard model of elementary particles. The superstring theorists adopted the Kaluza-Klein theory a few years later, but both groups of theorists have expanded the number of dimensions to 10,11or more. However, these scientists have never demonstrated that adding the extra dimensions above Kaluza's original five would remain consistent with the original purpose of Kaluza's theory to unify general relativity and electromagnetism. These theories are untenable and speculative and they will remain so until superstring theorists can demonstrate that adding the extra dimensions does not alter the connection between Einstein and Maxwell's theories that Kaluza's five-dimensional structure established.
On the other hand, any extension of the Kaluza-Klein theory that is super- imposed on a quantum field theory should also suffer from fundamental problems because quantum field theories are by their very nature based upon a discrete model that is at odds with the assumed condition of continuity in Kaluza's original theory. Nor have the superstring theorists explained how the curvature of space-time fits into their theories, even though they take general relativity for granted as the basis of their theories. Any Kaluza or Kaluza-Klein theory that retains the infinitesimal (or Planck) extension of length in the fifth direction must deal with the same fundamental problem. The adoption of a real physical five-dimensional space-time structure, instead of a limited purely mathematical model, implies that curvature is an extrinsic characteristic of our common four-dimensional space-time continuum. However, an infinitesimally extended fifth direction seems to retain the intrinsic nature of the four- dimensional space-time by not explaining how the concept of curvature fits into the model, creating a paradox.
The superstring theories have evolved into the more general 'brane' theories. Several 'brane' theorists have speculated on all types of structures including dual three-dimensional branes, five-dimensional branes, colliding branes and curved branes within a bulk, to mention only a few examples. But it seems that they have yet to demonstrate whether these geometrical structures conform to the basic hypotheses upon which their theories depend, Kaluza's initial derivation of the general relativity and electromagnetic formulas from an extremely limited and conditional five-dimensional mathematical model of a continuous space- time. The Randall-Sundrum theory offers a case in point (Randall & Sundrum,
1999a, 1999b). In the Randall-Sundrum model, two branes are separated
1
540 J. E. Beichler
by a higher-dimensional bulk. One of the branes represents our common three-dimensional curved space, while gravitons traveling from our brane to the other brane are the only direct links between the branes. In one model, the second brane is an infinite distance away, effectively limiting our world to the single brane embedded in the bulk and guaranteeing a weak gravitational force. However, this model is in direct violation of Kaluza's condition that our four- dimensional world is closed with respect to the higher fifth dimension. Brane theories of this type must be required to demonstrate that their models do not disrupt the unification of electromagnetism and gravity in the Kaluza model upon which they are based. Yet no one has ever argued or even explored how such changes would affect the basic underlying principles of the original mathematical unification model developed by Kaluza.
The only theoretical research ever conducted to determine the mathematical consequences of changing Kaluza's theory only considered the relaxation of his initial suggestion of an infinitesimal extension, rather than changing any of his initial conditions. Einstein and Peter G. Bergmann completed this change in 1938 (Einstein & Bergmann, 1938). Einstein, Bergmann and Valentine Bargmann again considered it in 1941 (Einstein et al., 1941). They retained the 'closed loop' and 'equal length' conditions and remained within a continuous mathematical model of five-dimensional space-time, but allowed for the possibility of macroscopically extended lengths of the A-lines. Under these conditions, they were still able to derive Maxwell's formulas and thus maintain Kaluza's unification. But Einstein eventually gave up this avenue of research toward his goal of a unified field theory because he could not justify the notion of a normal sized fifth dimension that could not be sensed or detected in any manner. Even so, Einstein listed the five-dimensional approach as one of three possibilities to develop a unified field theory in his last published book before he died (Einstein, 1956). He stipulated that the five-dimensional hypothesis would only be tenable if it could be explained why the fifth dimension cannot be detected.
Conclusion
These three logical proofs, in themselves, will not immediately change the course of science. Science has ignored the implied existence of a real fourth spatial dimension for more than a century, so it will not be so easily compelled to accept it now. However, it is not just the three logical proofs that indicate the existence of a fourth spatial dimension to our universe. It is a preponderance of the evidence that will soon force science to accept the four-dimensional reality of space. The value of these three logical proofs will only become evident over [he lvnger term of scientific advances.
While logically proving the existence of a fourth dimension to space, these proofs also imply the geometric structure of that dimension relative to the other three. First of all, the fourth dimension of space would be different, like time, from the other three common dimensions of space. Otherwise, four- dimensionality would adversely affect the inverse square law and thus conflict
Five Dimensions of Space-Time 541
with normally accepted physical laws. Instead, the fourth dimension should be characterized by changing magnetic potential except inside elementary particles where the space curvature corresponding to matter would assume the shape of an exponential curve. Both of these characteristics imply that the total extension of space in the fourth direction cannot be infinitesimally small or even microscopic as in Klein's version of Kaluza's theory. The exponentially shaped singularity at the center of elementary particles such as protons would require a non- infinitesimal extension of space in the higher dimension.
In other words, if the magnetic potential and Yukawa potential exist in nature as described, then the fourth dimension of space, or the fifth dimension of space- time, cannot be infinitesimally extended. Both logical arguments imply that the extra higher dimension is macroscopically extended as Einstein, Bergmann and Bargmann demonstrated. It is provident that Kaluza's theory has already been developed as the basis for a new unification, but the macroscopic extension in the fourth direction of space means that the present unification theories that are based upon Kaluza's suggestion and Kaluza-Klein models are not valid. The path of unification that science must follow is the path that physics and nature leads us down, not the path that some scientists decide that nature must logically follow, no matter how 'beautiful' or aesthetically pleasing those theories might be. The path that nature has decided for science is the one that leads to the four- dimensionality of space (the Clifford model) and the five-dimensionality of the space-time continuum (the Einstein-Kaluza model).
Much of the early work on five-dimensional space was in an attempt to develop a theory that unifies the four fundamental interactions in nature: strong and weak nuclear forces, gravity and electromagnetism. German mathematician Theodor Kaluza and Swedish physicist Oskar Klein independently developed the Kaluza–Klein theory in 1921, which used the fifth dimension to unify gravity with electromagnetic force. Although their approaches were later found to be at least partially inaccurate, the concept provided a basis for further research over the past century.
Space-time--time couples Kaluza's five-dimensional geometry with Weyl's conformal space-time geometry to produce an extension that goes beyond what either of those theories can achieve by itself. Kaluza's ``cylinder condition'' is replaced by an ``exponential expansion constraint'' that causes translations along the secondary time dimension to induce both the electromagnetic gauge transformations found in the Kaluza and the Weyl theories and the metrical gauge transformations unique to the Weyl theory, related as Weyl had postulated. A space-time--time geodesic describes a test particle whose rest mass, space-time momentum, and electric charge q, all defined kinematically, evolve in accord with definite dynamical laws. Its motion is governed by four apparent forces: the Einstein gravitational force, the Lorentz electromagnetic force, a force proportional to the electromagnetic potential, and a force proportional to a scalar field's gradient d(ln phi). The test particles exhibit quantum behavior: (1) they appear and disappear in full-blown motion at definite events; (2) all that share an event E of appearance or disappearance do so with the same charge magnitude |q| = phi(E); (3) conservation of space-time--time momentum at such an event entails conservation of electric charge in addition to conservation of space-time momentum, among the participating particles; (4) at such events the d(ln phi) force infinitely dominates the other three --- this strongly biases the appearance and disappearance events to be concentrated deep in the discretely spaced potential wells of ln phi, and sparse elsewhere.
To explain why this dimension would not be directly observable, Klein suggested that the fifth dimension would be rolled up into a tiny, compact loop on the order of 10-33 centimeters. Under his reasoning, he envisioned light as a disturbance caused by rippling in the higher dimension just beyond human perception, similar to how fish in a pond can only see shadows of ripples across the surface of the water caused by raindrops.[2] While not detectable, it would indirectly imply a connection between seemingly unrelated forces. The Kaluza–Klein theory experienced a revival in the 1970s due to the emergence of superstring theory and supergravity: the concept that reality is composed of vibrating strands of energy, a postulate only mathematically viable in ten dimensions or more. Superstring theory then evolved into a more generalized approach known as M-theory. M-theory suggested a potentially observable extra dimension in addition to the ten essential dimensions which would allow for the existence of superstrings. The other 10 dimensions are compacted, or "rolled up", to a size below the subatomic level. The Kaluza–Klein theory today is seen as essentially a gauge theory, with the gauge being the circle group.
The fifth dimension is difficult to directly observe, though the Large Hadron Collider provides an opportunity to record indirect evidence of its existence. Physicists theorize that collisions of subatomic particles in turn produce new particles as a result of the collision, including a graviton that escapes from the fourth dimension, or brane, leaking off into a five-dimensional bulk. M-theory would explain the weakness of gravity relative to the other fundamental forces of nature, as can be seen, for example, when using a magnet to lift a pin off a table — the magnet is able to overcome the gravitational pull of the entire earth with ease.
Mathematical approaches were developed in the early 20th century that viewed the fifth dimension as a theoretical construct. These theories make reference to Hilbert space, a concept that postulates an infinite number of mathematical dimensions to allow for a limitless number of quantum states. Einstein, Bergmann and Bargmann later tried to extend the four-dimensional spacetime of general relativity into an extra physical dimension to incorporate electromagnetism, though they were unsuccessful.[1] In their 1938 paper, Einstein and Bergmann were among the first to introduce the modern viewpoint that a four-dimensional theory, which coincides with Einstein-Maxwell theory at long distances, is derived from a five-dimensional theory with complete symmetry in all five dimensions. They suggested that electromagnetism resulted from a gravitational field that is “polarized” in the fifth dimension.
www.scientificexploration.org/docs/21/jse_21_3_beichler.pdf
The main novelty of Einstein and Bergmann was to seriously consider the fifth dimension as a physical entity, rather than an excuse to combine the metric tensor and electromagnetic potential. But they then reneged, modifying the theory to break its five-dimensional symmetry. Their reasoning, as suggested by Edward Witten, was that the more symmetric version of the theory predicted the existence of a new long range field, one that was both massless and scalar, which would have required a fundamental modification to Einstein's theory of general relativity. Minkowski space and Maxwell's equations in vacuum can be embedded in a five-dimensional Riemann curvature tensor.
In 1993, the physicist Gerard 't Hooft put forward the holographic principle, which explains that the information about an extra dimension is visible as a curvature in a spacetime with one fewer dimension. For example, holograms are three-dimensional pictures placed on a two-dimensional surface, which gives the image a curvature when the observer moves. Similarly, in general relativity, the fourth dimension is manifested in observable three dimensions as the curvature path of a moving infinitesimal (test) particle. 'T Hooft has speculated that the fifth dimension is really the spacetime fabric.
<a href="https://en.wikipedia.org/wiki/Five-dimens
Breathless my heart is building a magic, a discrete tower of love...
Modelo: Gusy Bello
Franco Petrini Photography © 2010
Church of St Mary
Tomb of Baron William Bardolf and Lady Joan. Alabaster. Chapel of St Margaet, South aisle. Commissioned by Baron William around 1437, probably completed by 1447
Condition: the figures have suffered minor vandalism, but the colour of their robes has been restored discretely; figures have been removed from the now empty niches of the tomb chest
The tomb is set in St Margaret’s chapel, striking for its richly decorated parclose screen, mirrored in that of the chapel dedicated to the Virgin to the north. In 1437 Baron William established a chantry in the chapel, and in his will of 1438 arranged for his burial there. The tomb may have been in place by 1447, the date of Lady Joan’s will, in which she also arranged to be buried in the chapel.
The effigies are the best preserved of the pre-Reformation alabaster tombs in East Anglia
Baron William and Lady Joan recline with their hands clasped in prayer, looking up to heaven. Baron William rests his feet on the wings of an improbably duck-like eagle, while Lady Joan’s feet touch a fierce dragon, the emblem of St Margaret, to whom the chapel is dedicated. Baron William’s head is crowned by a chaplet and rests on his tilting helmet, while Lady Joan’s is on a pillow accompanied by two smaller angels. The effigies are well handled; the flow of her robes and tassels for the cloak are contrasted with the detail of his armour and gloves and both wear the SS livery collar, while he has the garter with the inscription ‘HONI SOIT QUI MAL Y PENSE’ on a blue ribbon on his left leg. The SS livery collar was not an insignia but a popular sign of allegiance, associated during the early fifteenth century with the House of Lancaster.
The splendour of the tomb reflects Baron Bardolf’s position; born William Phelip in 1383/4, on his mother’s side he was the grandson of the most powerful figure in East Anglia, Sir Thomas Erpingham, which, in the account in the ODNB, shaped his career.
Baron William had been lord of Dennington manor, which by the sixteenth century had passed to Sir Richard Wingfield, who sold it to Anthony Rous in 1538. There is a wall monument to Sir Thomas Rous (d.1619) kneeling in prayer opposite his wife on the south wall of the chapel, but by the mid seventeenth century Dennington Manor had been destroyed and Henham Hall, a large Tudor house built in 1538, which Anthony Rous had bought in 1548, became the seat of the Rous family (later ennobled as Earls of Stradbroke).
Richard and Sarah Cocke, The Public Sculpture of Norfolk and Suffolk, Liverpool University Press for the Public Monuments and Sculpture Association, 2013, pp.258-259
detail of Lady Joan Bardolf