واحد مشترک کمکی پژوهش و مهندسی «هوش یار-تواندار»     (HT-CSURE)

واحد مشترک کمکی پژوهش و مهندسی «هوش یار-تواندار» (HT-CSURE)

Hooshyar-Tavandar Common Subsidiary Unit for Research & Engineering
واحد مشترک کمکی پژوهش و مهندسی «هوش یار-تواندار»     (HT-CSURE)

واحد مشترک کمکی پژوهش و مهندسی «هوش یار-تواندار» (HT-CSURE)

Hooshyar-Tavandar Common Subsidiary Unit for Research & Engineering

مرور زندگی جورج کانتور دانشمندِ پرداخته به مفهوم بی نهایت ریاضی

جورج کانتور و اسرار بی نهایت


Georg Cantor

تاریخچه مفهوم شگفت انگیز بی نهایت، از گذشته های دور ذهن ریاضی دانان را به خود مشغول کرده بود. هر چند برخی معتقدند که مفهوم بی نهایت برای نخستین بار در تمدن هند باستان مطرح شده است، اما می توان گفت که نخستین کار جدی در مورد بی نهایت در عرصه ریاضیات به دوران یونان باستان و تحقیقات اقلیدس بر روی اعداد اول باز می گردد. اقلیدس در کتاب مشهور ” اصول ” خود هر چند مستقیماً نامی از بی نهایت نمی برد، اما به طور ضمنی به آن اشاره می کند که ” بزرگترین عدد اول، از حاصل ضرب هر تعداد مفروضی از اعداد اول هم بزرگتر است “. پس از اقلیدس، پژوهش در مورد بی نهایت توسط سایر ریاضی دانان همچنان ادامه یافت تا سرانجام نماد ∞ به عنوان نماد ابن مفهوم اسرارآمیز پا به عرصه ریاضیات گذاشت. با آغاز عصر جدید، پژوهش در مورد بی نهایت همچنان ادامه یافت. در این دوران ” گاتفرید ویلهلم لایبنیتز” و ” ایزاک نیوتن ” برای نخستین بار از وجود مفهوم جدیدی به نام ” بی نهایت کوچک ” در عرصه ریاضیات پرده برداشتند. بی نهایت کوچک که عملا از همان مفهوم بی نهایت مشتق شده است، عددی مثبت است که از هر عدد مثبت مفروض دیگری کوچکتر است. بدین ترتیب ” بی نهایت ” به همراه پسر عموی کوچک خود یعنی بی نهایت کوچک، پایه های عرصه بدیعی از ریاضیات به نام ” حساب دیفرانسیل و انتگرال ” ( حسابان) را شکل دادند و ابن گونه بود که بی نهایت عملا به مهمترین مفهوم در علوم و مهندسی جدید تبدیل شد. اما در حالی که دانشمندان و مهندسان به کاربردهای بی نهایت بسنده کرده بودند، تلاش برای کشف دیگر ویژگی های این مفهوم اسرارآمیز در عرصه ریاضیات همچنان ادامه یافت.

جورج والیدمر کانتور، پدر جورج کانتور، یک تاجر موفق بود که به عنوان یک عامل عمده فروش در پیترزبورگ و بعدها به عنوان یک دلال در بورس سهام پیترزبورگ کار می‌کرد. جورج والیدمر کانتور زاده‌ی دانمارک بود و عمیقاً به فرهنگ و هنر عشق می‌ورزید. ماریا آنّـا بـوم، مادر کانتور، روسی و بسیار اهل موسیقی بود. مطمئناً جورج استعداد قابل توجهی در موسیقی و هنر از والدینش به ارث برده بود چرا که او نیز ویلون زن برجسته‌ای بود. جورج درحالی که مادرش کاتولیک بود، پرورش یافته‌ی مذهب پدری‌اش؛ پروتستان بود.

کانتور تحصیلات مقدماتی را در خانه توسط یک معلم خصوصی فرا گرفت و پس از آن در پیترزبورگ به مدرسه‌ی ابتدایی رفت. او به همراه خانواده‌اش در سال ۱۸۵۶، زمانی که فقط یازده ساله بود؛ به آلمان کوچ کردند. با این وجود : «…او هرچند بقیه‌ی عمرش را در آلمان زندگی کرد و ظاهراً هرگز به زبان مادری‌اش چیزی ننوشته بود، اما با احساس غربت فراوانی سال‌های اولیه عمرش در روسیه را به یاد می‌آورد و هرگز در آلمان احساس آرامش نمی‌کرد…»

پدر کانتور سلامتی خوبی نداشت و با رفتن به آلمان، با آب و هوایی گرمتر از زمستان‌های سخت پیترزبورگ روبرو شد. آن‌ها در ابتدا در ویسبادن ساکن شدند، جایی که کانتور ژیمناستیک یاد گرفت؛ پس از آن به فرانکفورت نقل مکان کردند. کانتور در شهر دارمسد در مدرسه Realschule به صورت شبانه روزی تحصیل می‌کرد. در سال ۱۸۶۰ با یک کارنامه‌ی عالی از آن جا فارغ التحصیل شد. کارنامه‌ای که استعدادهای خارق العاده‌ی او را در ریاضیات و به ویژه در مثلثات، به خوبی نشان می‌داد. پس از کسب مدرکی از Höhere Gewerbeschule در شهر دارمسد در سال ۱۸۶۰، در سال ۱۸۶۲ وارد دانشگاه پلی تکنیک زوریخ شد. دلیل آن که پدر کانتور Höhere Gewerbeschule را برای پسرش انتخاب کرده بود، این بود که می‌خواست پسرش : «ستاره‌ای در آسمان مهندسی باشد …»

با این وجود کانتور در سال ۱۸۶۲ در پی کسب اجازه از پدرش برای ادامه تحصیل در ریاضیات در دانشگاه بود و هنگامی که سرانجام موافقت او را کسب کرد، بسیار خوشحال شد.
تحصیلات کانتور در زوریخ با مرگ پدرش در ژوئن ۱۸۶۳ خیلی زود قطع شد. سپس کانتور به دانشگاه برلین رفت و در آن جا با هرمان شوارتز همکلاسی بود و با او دوست شد. کانتور در جلسات سخنرانی وایراشتراس، کومر و کرونیکر حضور داشت. ترم تابستانی ۱۸۶۶ را در دانشگاه گوتینگن سپری کرد و برای اتمام پایان نامه‌اش در نظریه اعداد در سال ۱۸۶۷ به برلین بازگشت.

کانتور زمانی که در برلین بود با انجمن ریاضی رابطه‌ی زیادی داشت و طی سال‌های ۱۸۶۴-۶۵ رئیس انجمن بود. همچنین عضوی از یک گروه کوچک ریاضی بود که هفته‌ای یک بار نشست داشتند. کانتور پس از اخذ مدرک دکتری در سال ۱۸۶۷، در یک مدرسه دخترانه در برلین به تدریس پرداخت. سپس در سال ۱۸۶۸ به سمینار شلباخ که برای معلمان ریاضی بود، پیوست. در این مدت او روی پایان نامه تخصصی دکترای خود کار می‌کرد و بلافاصله پس از آن که در سال ۱۳۶۹ جذب هاله شد، این رساله‌ی خود را ارائه کرد که باز هم در نظریه اعداد بود و دکترای تخصصی خود را دریافت کرد.

موضوع تحقیقات کانتور در هاله از نظریه اعداد به آنالیز تغییر کرد. این تغییر به خاطر نقش هاینه، یکی از همکاران ارشدش در هاله بود که کانتور را برای اثبات مسأله حل نشده‌ای درباره‌ی یکتایی نمایش یک تابع به صورت یک سری مثلثاتی، به مبارزه طلبیده بود. این مسأله یک مسأله دشوار بود که بسیاری از دانشمندان از جمله خود هاینه و دیریکله، لیپشیتز و ریمان در مواجهه با آن ناکام مانده بودند. کانتور مسأله را حل کرد و یکتایی نمایش را تا آوریل ۱۸۷۰ ثابت کرد. در بین سال‌های ۱۸۷۰ تا ۱۸۷۲ مقالات بیشتری درباره‌ی سری‌های مثلثاتی منتشر کرد که همه‌ی آن‌ها تأثیرات تدریس وایراشتراس را نشان می‌دهد. کانتور در سال ۱۸۷۲ در هاله در حد یک پروفسور برجسته ریاضی ترفیع یافت و همان سال سرآغاز دوستی‌اش با ددکیند که او را در تعطیلاتی در سویتزرلند ملاقات کرده بود، شد. کانتور در سال ۱۸۷۲ مقاله‌ای درباره سری‌های مثلثاتی منتشر کرد که در آن اعداد گنگ را نسبت به همگرایی دنباله‌هایی از اعداد گویا تعریف می‌کند. در همان سال ددکیند تعریفش از اعداد حقیقی را با «برش‌های ددکیند» منتشر کرد و در این مقاله‌اش به مقاله‌ی سال ۱۸۷۲ کانتور که کانتور برایش ارسال کرده بود، ارجاع می‌دهد.

کانتور در سال ۱۸۷۳، شمارش پذیر بودن اعداد گویا را ثابت کرد یعنی می‌توانند با اعداد طبیعی در تناظر یک به یک باشند. همچنین نشان داد که اعداد جبری؛ اعدادی که ریشه‌های چند جمله‌ای‌ هایی با ضرایب عدد صحیح اند، شمارا هستند. اما تلاش‌هایش برای به نتیجه رسیدن این که آیا اعداد حقیقی شمارا هستند، سخت تر بود. او سرانجام در دسامبر سال ۱۸۷۳ ثابت کرد که اعداد حقیقی ناشمارا هستند و این موضوع را در مقاله‌ای در سال ۱۸۷۴ چاپ کرد.
تلاش های او در سال ۱۸۷۴ میلادی به نقطه عطفی رسید، زیرا در این سال بود که ” جورج کانتور ” ،ریاضی دان بزرگ روسی – آلمانی، به کشف حیرت انگیزی در مورد بی نهایت دست یافت: این که اگر چه بی نهایت، بی نهایت بزرگ است، اما با این حال بزرگتر از آن هم وجود دارد! این کشف، فوق العاده عجیب بود؛ چرا که می دانیم که بی نهایت از هر عدد قابل تصوّری بزرگتر است. پس چگونه ممکن است چیزی بزرگتر از بی نهایت هم وجود داشته باشد؟ در پاسخ باید گفت که هر چیزی که از بی نهایت بزرگتر باشد، اول از همه خودش باید بی نهایت باشد. بنابراین در واقع کانتور کشف کرد که بعضی بی نهایت ها از بعضی دیگر از بی نهایت ها بزرگتر هستند! اما به راستی چگونه ؟ آخر اگر بی نهایت، بی نهایت بزرگ است ، پس چگونه ممکن است بزرگتر از آن هم وجود داشته باشد؟! هنگامی که کانتور کشف عجیب و شگفت انگیز خود را برای سایر ریاضی دانان بازگو کرد،همگی تصور کردند که او دچار نوعی جنون شده است! به همین دلیل هم هنوز چند سالی از این کشف عجیب نگذشته بود که کانتور دچار افسردگی شدید شد. علت افسردگی شدید او کناره گیری از همکارانش و ناامید شدن از آنها و سایر ریاضی دانان بود؛ چرا که هرچه کشف مهم خود را برای آنها توضیح می داد،هیچ کس متوجه آن نمی شد در واقع این ریاضی دانان نسل بعد بودند که نهایتا به اهمیت فوق العاده کشف کانتور پی بردند. اما به راستی کانتور چگونه به چنین نتیجه حیرت انگیزی رسیده بود؟ پاسخ این معما به شاخه ای از ریاضیات باز می گردد که توسط خود کانتور بسط داده شده بود و امروزه ” نظریه مجموعه ها ” نامیده می شود.

تحلیل ریاضی بینهایت مفاهیم بنیادی دنباله عدد های صحیح مثبت …, ۱,۲,۳ نخستین و مهمترین نمونه از مجموعه های نا متناهی است. در اینکه این دنباله پایان یا انتها یا « نهایت»ی ندارد هیچ ابهامی وجود ندارد زیرا هر قدر عدد صحیح n بزرگ باشد، همواره می توان عدد صحیح بعدی ، n + 1 ، را تشکیل داد. اما در گذار از صفت « نا متناهی » یا « بینهایت » به اسم « بینهایت » نباید تصور کرد « بینهایت »، که معمولا با نماد ویژه ∞ نمایانده می شود، همچون یک عدد معمولی است. نمی توان نماد ∞ را در دستگاه اعداد حقیقی منظور کرد و در عین حال قواعد بنیادی حساب را محفوظ نگه داشت. با این حال، مفهوم بینهایت در همه جای ریاضیات حضور دارد زیرا اشیای ریاضی معمولاً نه به صورت انفرادی و جداگانه بلکه به عنوان اعضای رده ها یا توده هایی که بینهایت شی ء همنوع دارند ، مانند مجموعه عدد های صحیح یا عدد های حقیقی یا مثلث ها در یک صفحه، مورد مطالعه قرار می گیرند. به این دلیل، تحلیل دقیق بینهایت ریاضی ضرورت دارد. نظریه نوین مجموعه ها که در اواخر قرن نوزدهم به وسیله جورج کانتور و پیروان مکتب او خلق شده، به این مسئله پرداخته و توفیق خیره کننده ای در حل آن بدست آورده است. نظریه کانتور در باب مجموعه ها در بسیاری از شاخه های ریاضی رخنه کرده و در آن ها به شدت تاثیر گذاشته، و در مطالعه مبانی منطقی و فلسفی ریاضیات اهمیتی اساسی یافته است. نقطه شروع این نظریه مفهوم مجموعه یا توده است. منظور از این کلمه، هر گردآیه (مجموعه) ای از چیزهاست که با قاعده ای تعریف می شود که به دقت مشخص می کند کدام چیزها به گردآیه مفروض تعلق دارند. به عنوان مثال می توان از مجموعه همه اعداد صحیح مثبت، مجموعه همه کسرهای اعشاری دوره ای، مجموعه همه عدد های حقیقی، یا مجموعه همه خط های راست در فضا سه بعدی، نام برد.
مفهوم اساسی در مقایسه « اندازه » دو مجموعه، مفهوم « هم ارزی » است. اگر عضو های دو مجموعهA و B را بتوان چنان با هم جفت کرد که به هر عضو A یک و فقط یک عضو B و به هر عضو B یک و فقط یک عضو A نظیر شود، این تناظر را دو سویی می نامند و می گویند A و B هم ارزند. مفهوم هم ارزی برای مجموعه های متناهی با مفهوم معمولی برابری تعداد اعضا یکی است زیرا تعداد عضو های دو مجموعه متناهی یکی است اگر و تنها اگر بتوان تناظری بین آنها برقرار کرد. این موضوع در واقع همان ایده شمارش است زیرا وقتی مجموعه ای متناهی از چیز ها را می شماریم، صرفاً تناظری دو سویی بین آن چیزها و مجموعه ای از نمادهای عددی
  3،2،1… ، برقرار می سازیم. برای اثبات هم ارزی دو مجموعه متناهی همیشه لازم نیست اشیای موجود در آنها را بشمریم. مثلاًَ می توانیم بدون شمارش ادعا کنیم که هر مجموعه متناهی از دایره های به شعاع ۱ با مجموعه مرکز های آنها هم ارز است.
کانتور در سال ۱۹۱۳ بازنشسته شد و سال‌های آخر عمر خود را با بیماری و کمبود آذوقه به خاطر شرایط جنگی در آلمان سپری کرد. مراسم بزرگی برای تولد هفتاد سالگی کانتور در سال ۱۹۱۵ از طرف ‌هاله طراحی شده بود که به خاطر جنگ مجبور به لغو آن شدند ولی مراسم کوچکی در خانه‌اش برگزار شد. کانتور در ژوئن ۱۹۱۷ برای آخرین بار به آسایشگاه رفت و مکرراً در نوشته‌هایش به همسرش از او می‌خواست تا موافقت کند که به خانه برگردد. او به علت سکته قلبی درگذشت.

منبع : http://en.wikipedia.org/wiki/Georg_Cantor

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SONY & Other Corporations Have Been Quietly Researching & Developing Technology Based On ESP-***

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“We didn’t know how to explain it, but we weren’t so much interested in explaining it as determining whether there was any practical use to it.”

The quote above comes from Major General Edmund R. Thompson, Army Assistant Chief of Staff for Intelligence from 1977-81. He was referring to the investigation of “psychic phenomena,” otherwise known as psi. Psi includes the study of intuition, mind-body connection, psychokinesis, telepathy, precognition, clairvoyance, remote viewing, and much more.

Although hundreds of peer-reviewed studies have produced statistically significant results in this realm over the decades, psi is still greeted with unwarranted skepticism and disbelief.

“The discovery of truth is presented more effectively, not by the false appearance of things present and which mislead into error, not directly by weakness of the reasoning powers, but by preconceived opinion, by prejudice.”

– Arthur Schopenhauer, German philosopher (1788-1860)

The 1995 declassification of the U.S. Government’s Stargate Program, which studied remote viewing — the ability of a person to describe a remote geographical location up to several hundred thousand kilometers from their actual physical location — proved their ongoing interest in this subject. This program lasted more than two decades, and was used multiple times, successfully, to collect intelligence from various locations.

They also studied precognition. Physicist and author Russell Targ, who pioneered the development of the laser and laser applications, also co-founded this program in conjunction with the Stanford Research Institute (SRI). You can view a recent talk he gave that was cancelled by TED, “Everything I know About ESP,” here.

When this program was declassified, the American Institutes for Research reviewed it, and both reviewers concluded:

The statistical results of the studies examined are far beyond what is expected by chance. Arguments that these results could be due to methodological flaws in the experiments are soundly refuted. Effects of similar magnitude to those found in government-sponsored research at SRI and SAIC have been replicated at a number of laboratories across the world. Such consistency cannot be readily explained by claims of flaws or fraud.

Even as far back as 1985, a report prepared by the Army Research Institute disclosed that “the data reviewed in this report constitute genuine scientific anomalies for which no one has an adequate explanation for.”

A 1999 a statistics professor at UC Irvine published a paper showing that parapsychological experiments have produced much stronger results than those showing a daily dose of aspirin helps prevent a heart attack.

The list goes on and on, and with such obvious and credible results in the field, it’s clear that not only governments, but big corporations, like Sony, would want to capitalize on this too.

“These disturbing phenomena (ESP) seem to deny all our scientific ideas. How we should like to discredit them! Unfortunately the statistical evidence, at least for telepathy, is overwhelming.”

According to Dr. Dean Radin, Chief Scientist at the Institute of Noetic Sciences, which was founded by Apollo 14 astronaut Dr. Edgar Mitchell, “Quiet research programs examining thee and other exotic technological possibilities have been under way for several years in academic and industrial laboratories.”

He shares this information in one of his books, The Conscious Universefrom which I obtained the quotes and information below. It’s an extremely fascinating read, and this article doesn’t do it any justice, so please check it out if you’re interested in these types of phenomena.

“Action at a Distance,” or the ability of mind to influence matter, is very real, and has tremendous implications.

In his book, Radin cites a story that appeared in the December 10, 1995 issue of the South China Morning Post — the same year the U.S. government declassified the Stargate Program, mentioned above:

SONY, the corporation which revolutionized the world of audio and electronics, has acknowledged it is conducting research into alternative medicine, spoon bending, X-ray vision, telepathy and other forms of extra-sensory perception (ESP).

The institute of Wisdom was founded in 1989 at the instigation of Sony’s founder. . . . The company believes it has proved the existence of ESP, and is already developing a diagnostic machine based on the principles of oriental medicine. . . .

A sub-division of the institute, Extra-Sensory Perception Excitation Research, has worked with more than 100 possessors of ESP. In one test, subjects were presented with two black plastic containers, one of them containing platinum, the other empty. Psychic individuals were able to “see” the platinum seven times out of 10.

Yoishira Sako, a former specialist in artificial intelligence who heads the four man research team, believes commercial applications could apply to his research. “We haven’t come up with such great results so far, he said, “But if we eventually discover that ki energy is based on a kind of information transmission, it would lead to a complete energy revolution. If we can understand the mechanisms of telepathy, it would totally transform communication methods.

This was more than a decade ago, and with all of this research being locked up in Special Access Programs (read more about those here) or otherwise hidden, how are we ever going to have any transparency? Radin makes this point in his book, and highlights how corporations are the same way, reluctant to publicize their interests and findings. But he does provide two more examples, Bell Laboratories and the Contel Technology Centre:

At Bell Labs in the 1980s, I explored mind-matter interaction effects to see whether certain electronic circuits might be susceptible to psi influences, some aspects of this research achieved the Bell Labs imprimatur. At Contel in the early 1990s, I began to experiment with commercially-available, off the shelf electronics to see if ordinary components were susceptible to psi influences. This was an important first step toward building psi based devices, because unless scientists are able to demonstrate proof of principle with existing hardware and software, they will have no hope of obtaining funding to create speculative, custom-made microelectronics from scratch.

He then goes on to share his experience developing a random key for a highly secure data encryption method, where he used a random number generator on a single chip.

“I conducted two psi experiments using this chip, and both were successful in demonstrating mind-matter interaction influences precisely where I had predicted they would appear.”

A prototype was then built, approved, and tested. The test consisted of 10 volunteers who were asked to mentally influence the random system in strictly prescribed ways, and eventually, a patent disclosure was prepared.

“Unfortunately, immediately after we complete the prototyping tests, GTE corporation merged with Contel, and the disruption of the merger halted our efforts on this project.”

*** Quantum Theory Predicts That The Future Could Be Influencing The Past

Quantum Theory Predicts That The Future Could Be Influencing The Past (Yes You Read That Correctly)


Physicist and Nobel laureate Richard Feynman once said, “We choose to examine a phenomenon which is impossible, absolutely impossible, to explain in any classical way, and which has in it the heart of quantum mechanics. In reality, it contains the only mystery.”


And it’s true. Multiple theories, such as quantum entanglement, have exited the theoretical realm and been confirmed within the mainstream. Even browsing through some previously classified documents in the CIA’s electronic reading room, you can see how Black Budget science confirmed some of these topics decades ago, yet we never heard about it through the mainstream. Here is a prime example of a document on quantum entanglement. From this document we can see that its existence was confirmed decades ago.

What’s also interesting about that document is that it discusses telepathy, a phenomenon directly related to and made possible by discoveries within quantum physics. “Parapsychology” pr “Psi” and quantum physics go hand in hand.

Now, a recent paper, published in Proceedings of The Royal Society Asupports the argument that quantum theory must be “retrocausal,”or that an effect can occur before its cause.

Hard to wrap your head around, isn’t it? But just because something cannot be understood, does not mean it isn’t real, and we shouldn’t dismiss things we don’t understand. This is often seen with concepts like telepathy, even though they’ve been confirmed and verified, if covertly.

Take this document, for example, which examines the “paranormal ability to break through spatial barriers.”

Lis Zyga from Phys.org points out the appeal of retrocausality:

First, to clarify what retrocausality is and isn’t: It does not mean that signals can be communicated from the future to the past—such signaling would be forbidden even in a retrocausal theory due to thermodynamic reasons. Instead, retrocausality means that, when an experimenter chooses the measurement setting with which to measure a particle, that decision can influence the properties of that particle (or another particle) in the past, even before the experimenter made their choice. In other words, a decision made in the present can influence something in the past.

Clearly, if this theory is correct, our concept of “time” is flawed — physical processes can actually run forward and backwards while being described by the same physical laws.

Zyga, however, makes some comments that show a lack of awareness with regards to certain concepts, as she argues that “the whole idea of retrocausality is so difficult to accept because we don’t ever see it anywhere else. The same is true of action at a distance.”

Action at a distance is the idea that physical systems can be moved, changed, or influenced without being physically touched by anything else. It refers to the nonlocal interaction of objects that are separated in space. Again, this has been shown to be a real phenomenon, and it’s been well documented multiple times. So, the statement that “we don’t really see it anywhere else” actually isn’t true.

Another great example, using quantum systems, comes from a paper published in the peer-reviewed journal Physics Essays. It explains how this experiment has been used repeatedly to explore the role of consciousness in shaping the nature of physical reality.

It was published by Dr. Dean Radin, who you will see in the lecture below. He’s the chief scientist at the Institute of Noetic Sciences.

He produced incredible results: Human intention, via meditators, was able to actually collapse the quantum wave function. The meditators were the “observer” in this case.

In fact, as Radin points out in his lecture, a “5 sigma” result was able to give CERN the Nobel Prize in 2013 for finding the Higgs particle (which turned out not to be Higgs after all). In this study, they also received a 5 sigma result when testing meditators against non-meditators in collapsing the quantum wave function. This means that mental activity, the human mind,  attention, and intention, which are a few labels under the umbrella of consciousness, compelled physical matter to act in a certain way.

“Observations not only disturb what has to be measured, they produce it. . . . We compel [the electron] to assume a definite position. . . . We ourselves produce the results of the measurement.”

If this weren’t true, then why, for example, would the American Institutes for Research arrive at the following conclusion about action at a distance?:

The statistical results of the studies examined are far beyond what is expected by chance. Arguments that these results could be due to methodological flaws in the experiments are soundly refuted. Effects of similar magnitude to those found in government-sponsored research at SRI and SAIC have been replicated at a number of laboratories across the world. Such consistency cannot be readily explained by claims of flaws or fraud.

Even as far back as 1985, a report prepared by the Army Research Institute disclosed that “the data reviewed in this report constitute genuine scientific anomalies for which no one has an adequate explanation for.”

This new paper, published by Matthew S. Leifer from Chapman University in California and Mathew F. Pusey from the Perimeter Institute for Theoretical Physics in Ontario, Canada, wanted to find out if time, like matter, behaves differently at the quantum scale.

The researchers developed a model, based on action at a distance, where they exchanged space for time. So, as entanglement shows, there is really no separation between objects, or information is actually travelling faster than the speed of light.  But, if causality ran backwards, this would posit that the particle in the present could actually affect the particle that it was/is entangled with, back through time. Meaning that, not only are two particles connected, showing that space is just the concept that provides the illusion of separation, they are also still “entangled,” regardless of time, which is why there are quantum theories predicting that what happens in the present can actually change what happened in the past.

The Delayed Choice/Quantum Eraser 

The delayed choice/quantum eraser experiment has been used multiple times, as well as repeated, to show how time doesn’t exist in the way we currently understand it. In 2007, (Science 315, 966, 2007) scientists in France shot photons into an apparatus and showed that their actions could retroactively change something which had already happened.

As Asher Peres, a pioneer in quantum information theory, once pointed out: “If we attempt to attribute an objective meaning to the quantum state of a single system, curious paradoxes appear: quantum effects mimic not only instantaneous action-at-a-distance, but also, as seen here, influence of future actions on past events, even after these events have been irrevocably recorded.” 

Wheeler’s Cosmic Scale Explanation of the Delayed Choice Experiment

John Wheeler uses a great analogy to illustrate a portion of this concept.

He asks us to imagine a star emitting a photon billions of years ago, heading in the direction of planet Earth. In between, there is a galaxy. As a result of what’s known as “gravitational lensing,” the light will have to bend around the galaxy in order to reach Earth, so it has to take one of two paths, go left or go right. Billions of years later, if one decides to set up an apparatus to “catch” the photon, the resulting pattern would be an interference pattern. This demonstrates that the photon took one way, and it took the other way as well.

One could also “peek” at the incoming photon by setting up a telescope on each side of the galaxy to determine which side the photon took to reach Earth. As we know from the double slit experiment, the very act of measuring or “watching” which way the photon comes in means it can only come in from one side. The pattern will no longer be an interference pattern representing multiple possibilities, but a single clump pattern showing “one” way.

What does this mean? It means how we choose to measure the “now” affects what direction the photon took billions of years ago. Our choice in the present moment affects what has already happened in the past.

Quantum entanglement exists, regardless of time, which means two bits of matter (physical systems) can actually be entangled in time.














New theory of gravity might explain dark matter

New theory of gravity might explain dark matter

November 8, 2016

New theory of gravity might explain dark matter

Credit: Wikipedia

A new theory of gravity might explain the curious motions of stars in galaxies. Emergent gravity, as the new theory is called, predicts the exact same deviation of motions that is usually explained by invoking dark matter. Prof. Erik Verlinde, renowned expert in string theory at the University of Amsterdam and the Delta Institute for Theoretical Physics, published a new research paper today in which he expands his groundbreaking views on the nature of gravity.

In 2010, Erik Verlinde surprised the world with a completely new theory of gravity. According to Verlinde, gravity is not a fundamental force of nature, but an emergent phenomenon. In the same way that temperature arises from the movement of microscopic particles, gravity emerges from the changes of fundamental bits of information, stored in the very structure of spacetime.


Newton's law from information

In his 2010 article (On the origin of gravity and the laws of Newton), Verlinde showed how Newton's famous second law, which describes how apples fall from trees and satellites stay in orbit, can be derived from these underlying microscopic building blocks. Extending his previous work and work done by others, Verlinde now shows how to understand the curious behaviour of stars in galaxies without adding the puzzling dark matter.

The outer regions of galaxies, like our own Milky Way, rotate much faster around the centre than can be accounted for by the quantity of ordinary matter like stars, planets and interstellar gasses. Something else has to produce the required amount of gravitational force, so physicists proposed the existence of dark matter. Dark matter seems to dominate our universe, comprising more than 80 percent of all matter. Hitherto, the alleged dark matter particles have never been observed, despite many efforts to detect them.


No need for dark matter

According to Erik Verlinde, there is no need to add a mysterious dark matter particle to the theory. In a new paper, which appeared today on the ArXiv preprint server, Verlinde shows how his theory of gravity accurately predicts the velocities by which the stars rotate around the center of the Milky Way, as well as the motion of stars inside other galaxies.

"We have evidence that this new view of gravity actually agrees with the observations, " says Verlinde. "At large scales, it seems, gravity just doesn't behave the way Einstein's theory predicts."

At first glance, Verlinde's theory presents features similar to modified theories of gravity like MOND (modified Newtonian Dynamics, Mordehai Milgrom (1983)). However, where MOND tunes the theory to match the observations, Verlinde's theory starts from first principles. "A totally different starting point," according to Verlinde.

Adapting the holographic principle

One of the ingredients in Verlinde's theory is an adaptation of the holographic principle, introduced by his tutor Gerard 't Hooft (Nobel Prize 1999, Utrecht University) and Leonard Susskind (Stanford University). According to the holographic principle, all the information in the entire universe can be described on a giant imaginary sphere around it. Verlinde now shows that this idea is not quite correct—part of the information in our universe is contained in space itself.

This extra information is required to describe that other dark component of the universe: Dark energy, which is believed to be responsible for the accelerated expansion of the universe. Investigating the effects of this additional information on ordinary matter, Verlinde comes to a stunning conclusion. Whereas ordinary gravity can be encoded using the information on the imaginary sphere around the universe, as he showed in his 2010 work, the result of the additional information in the bulk of space is a force that nicely matches that attributed to dark matter.


On the brink of a scientific revolution

Gravity is in dire need of new approaches like the one by Verlinde, since it doesn't combine well with quantum physics. Both theories, crown jewels of 20th century physics, cannot be true at the same time. The problems arise in extreme conditions: near black holes, or during the Big Bang. Verlinde says, "Many theoretical physicists like me are working on a revision of the theory, and some major advancements have been made. We might be standing on the brink of a new scientific revolution that will radically change our views on the very nature of space, time and gravity."


* Explore further: 3 knowns and 3 unknowns about dark matter

More information: Emergent Gravity and the Dark Universe, E. P. Verlinde, 7 Nov 2016. arxiv.org/abs/1611.02269

Provided by: Delta Institute for Theoretical Physics




 

A New And Unusual Force in The Universe Just Got Even Stranger



A New And Unusual Force in The Universe Just Got Even Stranger

The blackbody force is real.

MIKE MCRAE
24    MAY    2017
New research has expanded on the discovery of a strange phenomenon called blackbody force, showing that the effect of radiation on particles surrounding massive objects can be magnified by the space that warps around them.

The find could affect how we model the formation of stars and planets, and even help us finally detect a theoretical form of radiation that allows black holes to evaporate.

In 2013, physicists announced radiation emitted from objects called 'blackbodies' could not only nudge small particles away, but tug them closer. What's more, for hot-enough objects with only a small amount of mass, the pushing force could be stronger than their gravitational pull.

If you've never come across the term, a blackbody is any opaque object that absorbs visible light, but doesn't reflect or transmit it.

Technically, blackbodies describe theoretically perfect objects that cannot reflect any light at all. Physical examples such as the carbon nanotube materials used to make the crazy-looking Vantablack coatings come pretty close.

It'd be a mistake to think of all blackbodies as, well, black - they do emit radiation as their particles jiggle about, making them a useful way to describe an object's thermal properties.

Four years ago, a team of Austrian researchers figured out that the radiation emitted by a blackbody should have a rather curious effect on nearby atoms. 

To understand this effect, it helps to know that atoms can move and change direction when the photons they absorb cause a shift in their momentum. 

Given the right conditions, objects as large as a cell can be nudged around by a beam of light - a phenomenon commonly used in a form of technology called optical tweezers.  

Physicists have known for about a century that electromagnetic radiation can change the properties of nearby atoms through the Stark effect, which changes the positions of its electrons to sit in a lower energy state.

This happens to make them more likely to move towards towards the brighter parts of a beam of light.

The Austrian researchers put two and two together, showing how heat radiation could cause light to not only push particles away, but thanks to the Stark shift, they could also be pulled towards the object.

"The interplay between these two forces - a typically attractive gradient force versus repulsive radiation pressure - is routinely considered in quantum optics laboratories, but it was overlooked that this also shows up with thermal light sources," lead researcher Matthias Sonnleitner from the University of Innsbruck told Phys.org back in 2013.

While force is incredibly weak, they also showed that the radiation's net pulling power could actually be greater than the tiny amount of gravity produced by minuscule, hot objects, having implications for particles smaller than a dust grain.

"These sub-micron-sized grains play an important role in the formation of planets and stars or in astro-chemistry," said Sonnleitner.

"Apparently, there are some open questions on how they interact with surrounding hydrogen gas or with each other. Right now, we are exploring how this additional attractive force affects the dynamics of atoms and dust."

Fast-forward to now, and another team of physicists has taken up where Sonnleitner and his colleagues left off, exploring the effect of both the blackbody's shape and its effect on the curvature of surrounding spacetime on this optical attraction and repulsion.

In particular, they calculated the warping of space - or topology - around a spherical and a cylindrical blackbody, and measured how the differences might affect the blackbody radiation forces.

They found the curvature of the spherical blackbody and the topology of space surrounding it had a magnifying effect on the attractive force due to both the effect of gravity and the angle at which the radiation struck the particles.

This wasn't the case for the cylinder, with its flat surface and surrounding space, where the blackbody effect wasn't magnified.

While the effect wouldn't be detectable in the laboratory, or even for objects the size of our Sun, for massive blackbody objects like neutron stars or more exotic forms of space-bending physics, this effect could make a significant difference.

"We think that the intensification of the blackbody force due to the ultradense sources can influence in a detectable way the phenomena associated with them, such as the emission of very energetic particles, and the formation of accretion discs around black holes," lead researcher Celio Muniz from Ceará State University, Brazil, explained to Phys.org.

The team also applied the previous findings on the blackbody force to a concept called a global monopole - a theoretical point similar to an electric charge, which affects the shape of surrounding space without gravity - as well as another theoretical warping of space called a cosmic string.

"This work puts the blackbody force discovered in 2013 in a wider context, which involves strong gravitational sources and exotic objects like cosmic strings as well as the more prosaic ones found in condensed matter," Muniz said.

This research was published in Europhysics Letters.