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FAQs
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What are the best productivity tools for entrepreneurs?
I now accept Suggested Edits, as they come in. Include the price of the product/service.Pre Launch:Javelin. Start and grow your product faster. javelin.com/?ref=p5eybNFKResearch:Clipular http://www.clipular.com (free)Evernote http://www.evernote.com. Free, and $45 per year.Launching Soon Page:LaunchRock http://www.launchrock.comLaunchSoon http://launchsoon.comLanding PagesSelf Hosted:ThemeForest http://www.themeforest.net $8+Hosted:UnBounce (landing pages) http://www.unbounce.com $50/moKickOffLabs: http://www.kickofflabs.com/ $15/monthOptimizely: https://www.optimizely.com/ $17/monthTurnkey...
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What's the best comprehensive back office system for Real Estate brokerages that includes Transaction Management, CRM & Drip Ema
All brokers use some sort of software suite to help them continue on the go.“Approximately 71% agents responded that they did use some form of CRM service that is integrated with website and other 3rd party software like MLS & Zillow.”Right real estate software which is combination of CRM + Transaction Management + EMail application can be selected by doing feature-by-feature comparison only.Yet, successful sorting out of important features of an integrated back-office system is intimidating, especially to non-technical people.RealtyShine is bringing to your eyes real estate industry-specific suite of applications that you need to expect from a software vendor to avoid generic piece of property management solution:Tenant/contact managementTenant self-service portalsDocument management (lease agreements, 1099s, official notices, etc.)Native mobile applications for iOS, Android & WindowsProfessional web portal integrated with CRMRent payment processingWorkflow managementWork order/maintenance managementApplicant screeningAccounting and financial managementProspect/lead trackingLead scoringUnit inspection formsIntegration with ILS (internet listing service)Reporting and AnalyticsOnce shortlisted any property CRM, check out its Marketing Automation(MA) and Billing/Invoicing capabilities, because transaction management module may have been excluded from CRM, as you have already mentioned.Although many CRM providers boast to have added MA functionalities, they are quite limited in scope.At RealtyShine, we work passionately to make our customers look brilliant on reality space by delivering futuristic real estate tools that are fully web enabled.To know about pricing and plan, you can navigate to this page.
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Which tools help to boost work productivity?
First things first, from all the tools I use, I’m listing a few that save me an immense amount of time. Thus helping me focus on things that matter. Here goes my list:Pocket - A handy tool to save useful links. After a while, my bookmarks are just unorganised and Pocket made it simple to save links. I could save everything in one place and hence retrieval is easy. Also, If I ever come across something during work that might be a distraction, I Pocket it and read it later.Buffer - Primarily I use this to manage posts and content from our SM handles. I schedule posts at one time and never have to look at it again. This saves a lot of time as I can dedicatedly work on the content and push them to the pipeline.LearnBee - (Disclaimer: my team built it and I use it every day). I use it to find a specific work file quickly or to attach multiple work files in an email or to search for a file to show to the team during a meeting. The Chrome extension just saves me an immense amount of time, which I otherwise waste searching for a file.Jira and Trello - Both of these tools help me individually as well as my team to prioritize, organise and complete tasks in a better and efficient way.
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What do you do everyday to promote your website?
Great question!There are several ways that you can promote your website. Here are a few of my favorites:Schedule social media posts (blog articles, quotes, bit size content from your website) via Hootsuite to post on multiple channels such to get maximum signNow.Channels such as Facebook, Instagram, LinkedIn, TwitterLook up hashtags specific to your business on Twitter and engage with others or even better yet provide them a free resource that you’re giving away (preferably one that leads back to your site).Engage with people on Twitter, Facebook, LinkedIn, and Instagram by asking questions, answering questions, and starting new conversations.Pin new content on Pinterest a couple of times a week.There are many ways you can promote your website and it’s hard to not to get overwhelmed–so pick a few and give them a try. Once you’re ready you can always do more to promote.
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What are the best features of Microsoft Office 365?
Here’s a breakdown of some awesome Features Office 3651. Work Smarter, EverywhereAfter buying Office 365, you also gain access to its accompanying mobile apps and browser apps. This allows you to access their cloud service from any up to date web browser on your desktop or mobile device. Even better yet, you don’t have to install Office software on your computer to do this.The mobile app allows you to access all of your Office 365 subscriptions and Office products right from your smartphone or tablet; this includes Word, Excel, Powerpoint, Onenote, and more. Cut the cord and stop working on your PC only — download the Microsoft Office 365 mobile app to stay productive, even while on the go.2. Enjoy 50 GB of StorageEach Office 365 user receives a whopping 50 GB of storage with Exchange Online; this can be used to save emails, calendar events, task lists, meeting notes, contact information, and email attachments.You can save some more space in your mailbox by utilizing the OneDrive cloud storage feature to share attachments.Your OneDrive storage is also synced to your device, enabling you to work offline on files. As soon as you reconnect to the web, the newest versions of your documents will be automatically uploaded to your cloud storage. The new versions of your documents will also be sent to any other connected device, including your phone or tablet — nifty!3. Edit Documents with Real-Time Co-AuthoringCollaborate online and see changes your team makes to shared documents within your Office apps as they happen with the real-time co-authoring feature in Word. Save your file to OneDrive cloud storage or SharePoint so your team can access the document and make any necessary edits or updates. You can also share it directly from Word by utilizing a handily integrated sidebar. As the publisher and access-giver, you can edit accessibility settings at any time.With the improved version control that was rolled out with Office 2016 co-authoring, you can see which changes to the document were made by which contributor and when the update was made. You can also easily revert back to a previous version of the file whenever you need to.4. Connect with Co-WorkersYou may not have known this, but Office apps include a Skype in-app integration. You can use this feature to instant message your teammates, share your screen during meetings and have audio or visual conversations — without even exiting the Office apps you’re working in. You can continue Skype conversations even after you close your office apps via your desktop or mobile version of Skype. The best part? Your team will receive unlimited Skype minutes.Source: Microsoft5. Send Links, Not FilesIt’s time to move away from email attachments. It’s never been easier to share documents for co-authoring!Simply upload your file to Office 365’s cloud storage. Then, write your email via Outlook or the Outlook web app. Rather than attaching your document to the email, you can insert a link to the file on your cloud. Outlook will automatically allow email recipients to edit the document you wish to share. You can always change permissions on any document at your convenience.6. Convert OneNote Items into Outlook Calendar EventsEasily configure OneNote items to tasks within your Outlook calendar. You can also assign tasks to colleagues, complete with follow-up reminders and concise due dates. You can also transfer meeting notes taken in OneNote via email to your teammates, and add important details (date, location, and attendees) to their respective meeting.7. Use Your Mouse as a Laser Pointer during PowerPoint PresentationsWith only a simple keyboard shortcut (Ctrl + P), your mouse can be used as a laser pointer during your PowerPoint presentations. You can also use the “presenter mode” commands while using this feature.The laser pointer tool has been a nifty trick within older versions of the office apps for years; however, it was only recently integrated for touch-screen devices. All you have to do is hold down on your device’s screen, and the laser pointer will appear.8. Create a Power Map Using ExcelTurn data into a 3-D interactive map with Power Map, one of the many Power BI-enhanced data visualization features that Excel has to offer. It comes with three different filters: List, Range, or Advanced. The Power Map will help you not only convey your data more effectively, but also support your claims by creating a tangible story from the numbers.
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What are the best ways to succeed massively in real estate?
You have to face the reality that you are heading back to school as the first year(s) are learning experiences. There are so many figures out there, like 80% of American agents leave in their first two years or something like that but it is reflective of people coming in with only a focus on making money and not a career.be open minded, learnbe trainable and then apply what you are taughchoose a broker not by the commission split but based on the training programBest, absolute best bet for success, get hired by a strong team, one with good leadership and one that is actually hard to get into. You will learn more working in a strong team in the first year than you will in five years on your own.If you join a team, who is their coach, Tom Ferry, Ken Goodfellow or whoever? If the team is not being coached by a top coach, do not bother, find a better team.Go to office meetings, learn what is happening, go to board and brokerage events, seminars, head to NAR Expos, absorb, learnI have been at it 50 years and I still sit down at lunch most days, when I am working in my home office and I turn on YouTube and watch a real estate or training video.Read the Millionaire Real Estate Agent and online, the remarkable, List More, Sell More by my favourite trainer, Jerry Bresser.If you put in less than 10 hours a day the first year, you are slackingCover as many open houses as possible for agents in your office but check them out first as some are dogs, or impossible to find even with 10 arrows pointing. Only cover saleable listings.Take a top producer to lunch. Not coffee, that is too cheap. If in the same office, ask if you can shadow her or him which some may allow. I spend as much time as I can with fellow top producers, their success and enthusiasm is contagious.DO not hang out with failed agents who bitch and complain. Do not walk away from them - run as fast as you canHave a great manager, someone who actually cares about your success and who will spend time with youI can go on and on. I was lucky, I was just 21, I got shoved into a hot subdivision, the commission per deal was terrible but we sold 5 or more a week so it paid off and I learned. I also observed that the money was in resale so I started to work hard to find buyers of new homes who had a resale to list. I knew nothing when I came in, there were no books, no tapes, nothing and I sold 100 houses my first year because I did what I set out here. I learned and at 50 years now I now know about 50% of what I need to know about real estate. I was recently at NAR Expo two months ago in Boston and took 11 seminars plus I got to hang out with top Realtors and I came back pumped and have put new things into my business.Very last thing, since 1968 I have been having a love affair with real estate. I have served some wonderful people, I have served some very difficult assholes as well (which gives one great stories to tell) and I have had incredible mentors along this journey. I could never make the money I do somewhere else, have reasonable hours, vacations and super friends because of this business. Either fall in love with you do or it will eat you up and spit you out.Your destiny and journey lies within you, No one is going to pull you through your first year. It is yours to seize.Best wishes for success, report back in one year and Merry Christmas, a real estate career can be a great gift for you and your family
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What would the "death" of a black hole look like? I've read that black holes lose mass due to Hawking Radiation ("evaporation").
Black holes are weird. They're so weird, Stephen Hawking says that much of what we know about them is probably fundamentally wrong!So let’s start by talking about suns, which are really just super-hot balls of mostly hydrogen collapsing through the sheer weight of their own gravity. This is known as nuclear fusion, and it occurs in the core, converting hydrogen to helium, and in larger suns, helium to carbon, carbon to neon and so on, making their way through the elements. Each of these changes causes a huge release of energy pushing against the gravity of the sun.This creates equilibrium between the gravity and energy, and can go on for billions of years, releasing energy and light to nearby planets. Eventually though, the core creates iron, which doesn’t release energy, so the energy to gravity equilibrium realigns.If there is a build-up of iron, gravity becomes a stronger force then the release of energy. When this happens, the sun implodes, releasing mass back into the core and causing a supernova explosion. The outcome is either a neutron star or a black hole.Now here is where it gets fun, because you can’t actually see a black hole. Instead we see nothing, no stars, no reflections - even light is swallowed up.Black holes don’t actually suck things up - they just swallow things that come into their path. For example, say our Sun turned into a black hole tomorrow, all of the planets in our Solar System would be safe from being sucked in by the dead Sun, but of course we’d still freeze to death without its warmth.The largest black hole we know of is 40 billion times the mass of our Sun.Black holes do eventually die due to a phenomenon known as Hawking Radiation , which is basically a build-up of quantum effects near the event horizon. For a better understanding of Hawking Radiation, check out my answer…Unnikrishnan Menon's answer to What is Hawking radiation?But this takes a very long time, and everything else in the Cosmos is predicted to have completely disappeared before the last black hole dies.Footnotes: Check out my blog…https://messinwithblackholes.quora.com?share=396067ef&srid=1QOF
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If Navy F-14 Tomcats were still active today, could they still fight the latest Russian fighters such as Su-35 and MiG-35?
The Tomcat was immortalized by Tom Cruise, who is still flying high- despite the curtain falling on the F-14 in 2006. The F-14 was the world's first 4th generation aircraft, while the Mikoyan MiG-35 and Sukhoi Su-35 are one of the last aircraft of the same generation. The most advanced F-14 D model would have stood very little chance of winning a visual, or beyond visual range combat against either Russian aircraft. Even in its heyday, the F-14 was an overrated aircraft, which gained enormous popularity due to the movie “Top Gun”. A majority of F-14 Tomcat were powered by the notorious TF-30 engine that gave it a lower thrust-to-weight ratio than the F-4 Phantom it was replacing (0.94 vs 0.87).Other than the Sukhoi Su-57, there is a scarcity of “clean sheet” aircraft designs since the demise of USSR. In contrast, the last “new” US 4th generation aircraft (F/A-18 Super Hornet) made it's first flight almost 25 years ago. Prior to the F-15X Advanced Eagle, the USAF had not purchased any 4th generation aircraft since 2001. Clearly, the US has arrived at the conclusion that 4th generation aircraft are a thing of the past. Russia, on the other hand, is financially incapable of replacing their fleet, due to a defense budget of $ 55 billion in 2018- which is 12,000% less than US defense budget. For most threat environments where 5th generation aircraft are not deployed, Russian 4+ generation aircraft can hold their own against western 4+ generation aircraft. By upgrading old designs with modern avionics, weapons, materials and small design changes, the cost per aircraft is much lower compared to western 4th generation aircraft.Compared to the simpler MiG and Sukhoi designs, the complex F-14 had a troubled gestation period, starting with the prototype crashing on its second flight in December 1970. A lack of orders also curtailed signNow development. During its 32 year service life, US Navy purchased 632 F-14, and over 150 of them were lost in accidents, causing considerable loss of life. In comparison to the F-14, Russian 4th generation aircraft are expected to serve till 2060 in several countries- about 55 years longer than the F-14.One of the biggest weaknesses of Russian combat aircraft continues to be their engine technology. Russian engines have considerably higher fuel consumption, far less reliability, and higher maintenance. This major technological weakness is owing to t.their inability to manufacture Single Crystal turbine blades till 2008. These Turbine blades were used on the re-engined F-14 D in 1986 when it was fitted with the GE F110 engine. Surprisingly, the 35 year old GE engine is more reliable than tin Klimov RD-33 engine fitted to the new MiG-35. Barring the AL-41F3/FU 30 engine being developed for the Su-57, the Saturn AL-41F-1S engine that is being used on the Su-35 is the highest technology Russian engine currently in regular service, and it features single crystal air-cooled turbine blades and a core operating temperature of over 2,600 F.The Su-35, which is derived from the Su-30, that was derived from the Su-27, is arguably the best 4th generation aircraft in the world. The Su-27 made its first flight in 1977, seven years after the F-14 Tomcat, and achieved full operational capability in 1985. The Su-27 became world’s most the most popular aircraft after it performed the stunning Pugachev's Cobra maneuver at the Paris air show in 1989. This maneuver left an indelible impression on aircraft enthusiasts worldwide. The Su-35 combat performance (on paper) is better than almost all contemporary 4+ generation aircraft. While extremely powerful, the Su-35 Passive electronically scanned array (PESA) radar is less stealthy compared to the newer AESA radar that is mated with the MiG-35. Both aircraft possess radars that are several degrees superior to the F-14D AN/APG-71 radar.The MiG-35 Fulcrum-F is an incremental upgrade to the MiG-29M. The MiG-29 first flew in 1977, seven years after the F-14, and became operational in 1982. MiG-35 was first flown in 2007. The MiG-35 costs approximately 50% of a comparable 4+ generation western aircraft. It is laced with several new technologies which include longer life airframe, fifth-generation information-sighting systems synthesis, ground attack ability, and a state of the art Phazotron Zhuk-AE AESA radar. The MiG-35 airframe is more robust, and infused with a considerable quantity of low weight composites. Armed with one of the world's most effective, medium range R-77 missile, (radar and IR) along with high quality IRST, The MiG-35 offers a better overall multi mission package compared to the older MiG designs. Due to it's increased fuel capacity, it boasts an improved combat range. This limitation had initially limited the original MiG-29 to point defense role. The MiG-35 provides 100% greater weapons payload capacity over the original model. This makes the MiG-35 the highest performing MiG aircraft to date.Regardless of the commercial and technological failure of the F-14, many current fighter aircraft technologies can trace their origin in the F-14. Despite that, the MiG-35 and Su-35 would have outclassed it in dogfight. Both Russian aircraft have off-boresight missile firing capability, Helmet Mounted Cueing system, thrust vectoring engines and faster, more maneuverable IR homing missiles. They also have extremely good sustained and instantaneous turn rates, and stall resistant high AOA capability, better aerodynamics, FBW controls, thrust vectoring, more modern wing design and a much higher thrust to weight ratio. The Tomcat would have unfortunately met its Waterloo in a visual dogfight very quickly!The F-14 was designed in an era when ships were at the mercy of cruise and anti-ship missiles. The F-14 had a 550 nautical mile combat radius, in order to intercept Soviet bombers before they could launch their missiles at US ships. The Sukhoi Su-35 has the largest combat radius of all three aircraft. While the F-14 was armed with the AIM-54 Phoenix long-range missile that could hypothetically intercept attacking aircraft at a range of 100 nautical miles. During its operational history, the F-14 failed to down a single Iraqi aircraft in the 6,600+ sorties flown by almost 100 F-14’s. The dismal performance of the Phoenix would have left the F-14 with only AIM-7M Sparrow missiles, which are out ranged by the Russian R-77 missiles. Even if the F-14 would have been successful in locking on to an Su-35 or MiG-35 with its Phoenix missiles, the combination of brute power and high quality avionics in both Russian aircraft would have allowed them to evade the missile by turning “cold” to the incoming missile. The F-14D’s ALQ-165 jamming pod would not have any signNow impact on the the defensive/offensive capability of either Russian aircraft. If anything, the Russian R-77 missile “home-on-jam” capability would have helped guide the Russian missiles to the F-14 through its own jamming beam!In conclusion, the Su-35 is the best Russian fighter aircraft in service, and it can easily match the best 4+ generation aircraft in service today, including the Eurofighter Typhoon and the French Rafale. That equation is likely to change heavily in favor of European 4+ generation aircraft with the introduction of the Meteor BVR missile. The Russian pair is leaps ahead of the F-14, despite the movie “Top Gun” turning the F-14 into an invincible interceptor, and Tom Cruise into a household nameThe US and USSR defence spending (above) during the the cold war. Russian spending is in red color.The US and Russian post cold war defense spending (above). At present, Russia spends far less on defense compared to the USA, which has left them far behind in development and deployment of high quality military hardware.A guided tour of the F-14B (above)Airframe size and design comparison between Mig 29 and Mig 35 (above)MiG-35 video preview (above)The Su-35 (above) performing the signature “Pugachev Cobra” maneuver.References:Mikoyan MiG-35The Sukhoi Su-35 - How It Stacks Up To The CompetitionGrumman F-14 TomcatTop GunF-14 Tomcat - Airforce TechnologyPratt & Whitney TF30F-22 Raptor vs Sukhoi SU-35Turbine bladeF-14DKlimov RD-33 - WikipediaSaturn AL-31 - WikipediaPugachev's CobraPassive electronically scanned arrayUnderstanding AESA: A Game-Changer in RADAR TechnologyF-14 RadarMiG-35 Fulcrum-F: A Lemon from RAC MikoyanAssessing Russia's First AESAThe world’s most effective air-to-air missilesR-77 - WikipediaYou Thought Cooking Your Turkey Was Tough? Try Maintaining An F-14!Sukhoi Su-35 (Flanker-E / Super Flanker) Multirole Heavy Combat Fighter Aircraft - RussiaAIM-54 Phoenix - WikipediaF-14 Tomcat operational history - WikipediaAIM-7 Sparrowhttps://fas.org/man/dod-101/sys/...METEOR - MBDASukhoi Su-57 - WikipediaUSAF's Next Budget Request Will Include New F-15X Advanced Eagle Fighter Jets: ReportGeneral Electric F110 - Wikipedia
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Is wave-particle duality an illusion?
"Illusion" is an interesting choice of words. To acquire the kind of understanding I think you're after, let's back up a bit and see if we can excavate the foundation of this question. Let me start with a quote. “The voyage of discovery lies not in seeking new horizons, but in seeing with new eyes.” ~ Marcel Proust An examination of the double-slit experiment will give us a good introduction to the mystery you have singled out. But to make that examination worthwhile, we need to make sure that we are familiar with an important effect known as interference. [i]Interference applies universally to all interacting waves. A water wave, for instance, can be described as a disturbance in the shape of the water’s surface. This disturbance produces regions where the water level is higher and regions where it is lower than the undisturbed value. The highest part of each ripple is called a peak and the lowest part is called a trough. Typically waves involve periodic succession, peak followed by trough followed by peak and so on. In general, we can define a wavelength as the distance between identical parts of adjacent waves. Measurements from peak to peak, or trough to trough, for example, give the same value for wavelength.Figure 1 Peaks and troughs of wavesWhen waves interact in a medium, they interfere. For example, if we drop two rocks into spatially separated parts of a pond, their waves will interfere when they cross. (Figure 2) When a peak of one wave and a peak of another wave come together, the height of the water rises to a height equal to the sum of the two peaks. Similarly, when a trough of one wave and a trough of another wave cross, the depression of the water's surface dips to the sum of the two depressions. And when a peak of one wave crosses with a trough of another, the (at least partially) cancel each other out. The peak of one wave contributes a positive displacement while the trough of the other wave contributes a negative displacement. If the two waves have equal magnitude, then there will be perfect cancelation and the water's surface will be flat, just as it was before any wave existed.Figure 12-2 Constructive and destructive interference Keeping these rules of interference in mind, let’s turn our attention to light. If we take a laser emitting a single wavelength—a single color, and shine it on a screen that has a slit etched into it (Figure 3), what image should we expect to see on the wall behind the screen? [ii] Classically speaking, we would expect to see a stripe of light on the wall. (Classically means according to our four-dimensional intuition, or the rules of Euclidean geometry.) It turns out that this is what we see. In this sense light’s behavior correlates perfectly with our Euclidean intuition.Figure 12-3 Expected single slit projectionWhat image should we expect to see on the wall if we etch a second slit on our screen and cover the first slit with a black piece of tape? Well, our classical intuitions tell us to expect a line of light projected on the wall, just like we did before, except this line of light should be offset from the first. Again, this is exactly what we see when we perform the experiment. So far all of this is straightforward and conceptually trivial. But as it turns out, we are only one step away from a profound mystery. We discover this mystery by removing the piece of tape. To understand the impact of this mystery, ask yourself: What sort of projection do we expect to see on the wall when both slits are open?Classical intuition tells us that we should see two parallel bands of light on the wall (Figure 4).Figure 4 Expected double slit projectionBut this is where our classical training (our Euclidean intuition) lets us down. This is also where classical mechanics breaks down. When we perform this experiment, something completely counterintuitive happens, contradicting our Euclidean intuitions. A distinct interference pattern is projected on the wall (Figure 5).Figure 5 Actual double slit projection The bright and dark bands produced in this double-slit experiment are telltale signs that light propagates as a wave. [iii] Interference patterns are key signatures of waves. The problem is that this wavelike characteristic directly clashes with our observations of light’s particulate behavior. After all, photons are always found in point-like regions rather than spread out like a wave, and individual photons are always found to have very discrete amounts of energy. When measuring a wave, you would expect to find its energy spread out over a region instead of being concentrated in one location. So how are we supposed to make sense of this observation? What is going on?These diametrically opposed properties of light are verified facts. Contradictory as they may seem, they are here to stay. They have forced us to the seemingly paradoxical conclusion that light is both a wave and a particle. But how can this be? How can it be both? Although many scientists have found thewave-particle duality of light to be conceptually vague and schizophrenic, this description has persisted. In fact, after the wave-particle concept was adopted as an accurate description of light, it was extended to describe electrons and, eventually, all of matter. This transition was nothing short of a revolution.Up until 1910, atoms were simplistically viewed as miniature solar systems with the nucleus making up the “central star” and orbiting electrons being “planets”. [iv] The wave-particle duality of light and matter rejected this view and pointed to a signNowly different architecture for atoms. Of course, this conceptual transition did not take hold over night.In 1924, Prince Louis de Broglie found that in addition to their particle like character, [v] electrons also possessed a wavelike character. In 1927, Clinton Davisson and Lester Germer followed this up by firing a beam of electrons at a piece of nickel crystal, which acted as a barrier analogous to the one used in the double-slit experiment. A phosphor screen recorded the resultant pattern of electrons. [vi] When they examined the screen, they observed an interference pattern just like the one produced in the double-slit experiment, showing that even electrons have wavelike properties.These experiments shook the foundation of physics by threatening the structure of classical mechanics and destroying humanity’s intuitive framework of reality. But it didn’t stop there. The next step was to tune the beam of electrons down so that the electron gun fired just a single electron at a time. Similar experiments were later used with lasers wherein individual photons were fired seconds apart from each other. The results were mind-bending.Completely against expectation these experiments also produced interference patterns over time as the collection of electrons (or photons) continued to build (Figure 6).Figure 12-6 Over time individual photons construct an interference patternThese observations only added to the confusion. Waves are supposed to be a collective property—something that has no meaning when applied to separate, particulate ingredients. (A water wave, for example, involves a large number of water molecules.) So how can a single electron, or a single photon, be a wave? Furthermore, wave interference requires a wave from one place to interact with a wave from another place. So how can interference be relevantly applied to a single electron or photon? While we are considering such questions, we should also ask, if a single electron or photon is a wave, then what is it that is “waving”? [vii]To answer these questions, Erwin Schrödinger proposed that the stuff that makes up electrons might be smeared out in space and that this smeared electron essence might be what waves. If this idea was correct then we would expect to find all of the electron’s properties, spread out over a distance, but we never do. Every time we locate an electron, we find all of its mass and all of its charge concentrated in one tiny, point-like region. Max Born came up with a different idea. He suggested that the wave is actually a probability wave. [viii] Einstein tinkered with a similar idea when he hypothesized that these waves were optical observations that refer to time averages rather than instantaneous values. Inserting a probability wave (also called a state vector, or a wave function) as a fundamental aspect of Nature delivers another blow to our common-sense ideas about how things truly operate. It suggests that experiments with identical starting conditions do not necessarily lead to identical results because it claims that you can never predict exactly where an electron will be in a single instant. You can only define a probability that we will find it over here, or over there, at any given moment. Two situations with the same probabilistic starting conditions, say of a single particle, might not produce the same results, because the particle can be anywhere within that probability distribution. From a classical perspective, the discovery that the microscopic universe behaves this way is absolutely baffling. Nevertheless, it is how we have observed Nature to be.This leads us to a rather interesting precipice. It seems that the map we have been using to chart physical reality somehow dissolves when we look closely at it. The rules of four-dimensional geometry simply fail to accurately map Nature when we examine the smallest scales. Nature doesn’t strictly behave as our old Euclidean map dictates. Stumbling upon this discovery forces us to face a vital question. Is Nature ultimately and fundamentally probabilistic in a way that we may never understand, as many modern physicists have chosen to believe; or, is this probabilistic quality a byproduct of our reduced dimensional representation of Nature?After pondering these questions long and hard, some physicists have come to believe that the tapestry of spacetime is analogous to water: that the smooth appearance of space and time is only an approximation that must yield to a more fundamental framework when considering ultramicroscopic scales. As far as I can tell, however, up until now this point has only been entertained abstractly. Geometrically resolving a molecular structure for space might resolve our greatest quantum mechanical mysteries, but as of yet, no one has taken that final step. No one has developed a self-consistent picture from this geometric insight. No one has moved beyond the mathematical suggestion that spacetime is analogous to water, or interpreted the theoretical quanta of space as being physically real. Consequently, a framework that enables conceptualization of what is meant by the “molecules” or “atoms” of spacetime has not been developed.Eight decades of meticulous experiments have confirmed the predictions of quantum mechanics based on this wave function, or probability wave, description with amazing precision. “Yet there is still no agreed-upon way to envision what quantum mechanical probability waves actually are. Whether we should say that an electron’s probability wave is the electron, or that it’s associated with the electron, or that it’s a mathematical device for describing the electron’s motion, or that it’s the embodiment of what we can know about the electron is still debated.” [ix]Although quantum mechanics describes the universe as having an inherently probabilistic character, we don’t experience the effects of this character in our day-to-day lives. Why is this? The answer, according to quantum mechanics, is that we don't see quantum events like a chair being here now and then across the room in the next instant, because the probability of that occurring, although not zero, is absurdly miniscule. But what exactly makes the probability for large things to act, as electrons do, so small? At what scales do such effects become important? And, why should the macroscopic universe be so different from the microscopic universe?As if these newly uncovered characteristics of reality weren’t obscure enough, quantum physicists conceptually fuddle things further by suggesting that without observation things have no reality. They claim that until the position of an electron is actually measured the electron has no definite position. Before it is measured, the position exists only as a probability, and then suddenly, through the act of measuring, the electron miraculously acquires the property of position.Einstein acutely recognized the absurdity of this claim. When approached with this conjecture, he famously quipped, “Do you really believe that the moon is not there unless we are looking at it?” [x] To him everything in the physical world had a reality independent of our observations. Measurements that suggested otherwise were mere reflections of the incompleteness by which we currently map and comprehend physical reality. To many quantum physicists, however, the unobserved Moon’s existence became a matter of probability. To them, a discoverable, complete map of physical reality, with the ability to resolve an underlying determinism, became nothing more than a myth—a romantic dream.The mathematical projection of quantum mechanics can be statistically matched with our four-dimensional observations, but when it comes to a conceptual explanation of those observations, it completely lets us down. Intuitive explanations cannot be gleaned from a framework of physical reality that is assumed to be fundamentally probabilistic. By definition, randomness blurs causality. This vague description of physical reality keeps us from grasping a deeper truth by allowing what should be the most basic of concepts to drip into a realm of nonsense.As an example of the confusion that stems from swallowing the standard quantum mechanical interpretation “guts, feathers, and all,” consider the fact that a probabilistic treatment of quantum mechanics leads us to the conclusion that the double-slit experiment can be explained by assuming that a photon actually takes both paths. We can combine the two probability waves emerging from both slits to statistically determine where a photon will land on a screen. The result mimics an interference pattern.According to this, we can explain interference patterns by assuming that one photon somehow always manages to go through both slits, but is this really what is going on? Does a photon really travel along both paths? Can this count as an explanation if we have no coherent sense of what it means? You might notice that if we were to design our experiment with three slits, then we would have to consider whether or not the photon really travels all three routes. This question can be extended for as many slits as you like, but the fundamental conceptual problem remains the same.In order to solve this mystery, you may suggest that we place detectors in front of the slits to determine if the photons are actually going through both slits, or just one. When we do this, we always find that individual photons pass through one slit or the other—never both. But, when we measure the position of individual photons we no longer get an interference pattern and so the question retains its ambiguity. Some have taken this to mean that the act of observation forces wave properties to collapse into a particle, but how and why this theoretical collapse occurs still lacks explanation.Because probability waves are not directly observable and because photons (and electrons) are always found in one place or another when measured, we might be tempted to think that probability waves might not be real—that they were never really there. If that is true, then how are the interference patterns created? Surely these probability waves exist, but in what sense? What are they referencing? Why is it that whenever we know which path the photon takes, we get a classical image instead of an interference pattern? How does the detection of a photon, or an electron, change its behavior?To date, these questions have yet to be resolved. In fact, more clever experiments designed to solve these questions have only deepened the mystery. For example, let’s perform the double-slit experiment again, but this time let’s place devices in front of the slits, which mark (but do not stop or detect) the photons before they pass through the slits. This marking allows us to examine the photons that strike the screen and subsequently determine which slit they passed through. Thus we only gain knowledge of which path the photon takes after the path has been completed. For some reason, however, when we do this we find that the photons do not build up an interference pattern. They form a classical image (Figure 4).Once again, it seems that “which-path” information inhibits us from probing these ghostly waves. But is it really the fact that we gain the ability to determine which path a photon goes through—independent of when we gain that information—that disrupts the interference pattern? Or does our marking of the photon somehow disrupt its interference potential?To explore this question, we perform what’s known as the quantum eraser experiment. We start with the same set up we just described. Then we place another device between each slit and the screen, which completely removes the mark from the photon. We already know that the marked photons project a classical image. Will an interference pattern reemerge if we remove the effects of this mark—if we lose the ability to extract the which-path information?When we perform this experiment the interference pattern does return (Figure 7). Does this mean that photons somehow choose how to act, based on our knowledge of them? Or does it imply something even stranger—that the photons are always both particles and waves simultaneously? How are we to understand either conclusion?Figure 12-7 An interference pattern Another curiosity of Nature is known as the photoelectric effect. Philipp Lenard first discovered this effect through controlled experiments in 1900. When light shines on a metal surface, it causes electrons to be knocked loose and emitted. Knowing this, Lenard designed an experiment that allowed him to control the frequencyof the incoming light. During the experiment, he increased the frequency of the light—moving from infrared heat and red light to violet and ultraviolet. Greater frequencies caused the emitted electrons to speed away with more kinetic energy. After discovering this, Lenard reconfigured his experiment to allow him to control the intensity of the incoming light. He used a carbon arc light that could be made brighter by a factor of 1,000.Because both experiments involved increasing the amount of incoming light energy he expected to have identical results. In other words, because the brighter, more intense light had more energy, Lenard expected that the electrons emitted would have more energy and speed away faster. But that’s not what happened. Instead, the more intense light produced more electrons, but the energy of each electron remained the same. [xi]In response to these experiments Einstein suggested that light is composed of discrete packets called photons. Under this assumption, light with higher frequency would cause electrons to be emitted with more energy, and light with higher intensity, that is, a higher quantity of photons, would result in emission of more electrons—just as we observe.The problem with this solution (a solution that is now universally accepted among physicists) is that it doesn’t provide us with a clear description for what the light quanta are. Why does light come in quantized packets? Near the end of his life Einstein lamented over this problem in a letter to his dear friend Michele Besso. He wrote, “All these fifty years of pondering have not brought me any closer to answering the question, what are light quanta?” [xii] It’s been another fifty years and we seem as confused as ever over how it is that light is quantized into little discrete packets called photons.In the midst of these enigmas lies the uncertainty principle, which states that knowledge of certain properties inhibits knowledge of other complimentary properties. For example, the more accurately we determine the position of an electron, the less we can determine its momentum, and vise versa.Heisenberg tried to explain the uncertainty principle by appealing to the observer effect; claiming that it was simply an observational effect of the fact that measurements of quantum systems cannot be made without affecting those systems. [xiii] Since then, the uncertainty principle has regularly been confused with the observer effect. [xiv] But the uncertainty principle is not a statement about the observational success of current technology. It has nothing to do with the observer effect. It highlights a fundamental property of quantum systems, a property that turns out to be inherent in all wave-like systems. [xv] Uncertainty is an aspect of quantum mechanics because of the wave nature it ascribes to all quantum objects.If our current description of quantum mechanics is fundamental, if there is nothing beneath the state vector—a claim that defines the heart of the standard interpretation of quantum mechanics—then this uncertainty principle may be a sharp enough dagger to kill our quest for an intuitive understanding of physical reality. The corrosive power of the uncertainty principle, when mixed with our current paradigm, is poignantly illustrated by an old story involving Niels Bohr. According to the story, Bohr was once asked what the complementary quality to truth is. After some thought he answered—“clarity.” [xvi] Unlike classical mechanics, which describes systems by specifying the positions and velocities of its components, quantum mechanics uses a complex mathematical object called a state vector (also called the wave function [xvii]) to map physical systems. Interjecting this state vector into the theory enables us to match its predictions to our observations of the microscopic world, but it also generates a relatively indirect description that is open to many equally valid interpretations. This creates a sticky situation, because to “really understand” quantum mechanics we need to be able to specify the exact status of and to have some sort of justification for that specification. At the present, we only have questions. Does the state vector describe physical reality itself, or only some (partial) knowledge that we have of reality? “Does it describe ensembles of systems only (statistical description), or one single system as well (single events)? Assume that indeed, is affected by an imperfect knowledge of the system, is it then not natural to expect that a better description should exist, at least in principle?” [xviii] If so, what would this deeper and more precise description of reality be?To explore the role of the state vector, consider a physical system made of Nparticles with mass, each propagating in ordinary three-dimensional space. In classical mechanics we would use Npositions and N velocities to describe the state of the system. For convenience we might also group together the positions and velocities of those particles into a single vector V, which belongs to a real vector space with 6N dimensions, called phase space. [xix]The state vector can be thought of as the quantum equivalent of this classical vector V. The primary difference is that, as a complex vector, it belongs to something called complex vector space, also known as space of states, or Hilbert space. In other words, instead of being encoded by regular vectors whose positions and velocities are defined in phase space, the state of a quantum system is encoded by complex vectors whose positions and velocities live in a space of states. [xx]The transition from classical physics to quantum physics is the transition from phase space to space of states to describe the system. In the quantum formalism each physical observable of the system (position, momentum, energy, angular momentum, etc.) has an associated linear operator acting in the space of states. (Vectors belonging to the space of states are called “kets.”) The question is, is it possible to understand space of states in a classical manner? Could the evolution of the state vector be understood classically (under a projection of local realism) if, for example, there were additional variables associated with the system that were ignored completely by our current description/understanding of it?While that question hangs in the air, let’s note that if the state vector is fundamental, if there really isn’t a deeper-level description beneath the state vector, then the probabilities postulated by quantum mechanics must also be fundamental. This would be a strange anomaly in physics. Statistical classical mechanics makes constant use of probabilities, but those probabilistic claims relate to statistical ensembles. They come into play when the system under study is known to be one of many similar systems that share common properties, but differ on a level that has not been probed (for any reason). Without knowing the exact state of the system we can group all the similar systems together into an ensemble and assign that ensemble state to our system. This is done as a matter of convenience. Of course, the blurred average state of the ensemble is not as clear as any of the specific states the system might actually have. Beneath that ensemble there is a more complete description of the system’s state (at least in principle), but we don’t need to distinguish the exact state in order to make predictions. Statistical ensembles allow us to make predictions without probing the exact state of the system. But our ignorance of that exact state forces those predictions to be probabilistic.Can the same be said about quantum mechanics? Does quantum theory describe an ensemble of possible states? Or does the state vector provide the most accurate possible description of a single system? [xxi]How we answer that question impacts how we explain unique outcomes. If we treat the state vector as fundamental, then we should expect reality to always present itself in some sort of smeared out sense. If the state vector were the whole story, then our measurements should always record smeared out properties, instead of unique outcomes. But they don’t. We always measure well-defined properties that correspond to specific states. Sticking with the idea that the state vector is fundamental, von Neumann suggested a solution called state vector reduction (also called wave function collapse). [xxii] The idea was that when we aren’t looking, the state of a system is defined as a superposition of all its possible states (characterized by the state vector) and evolves according to the Schrödinger equation. But as soon as we look (or take a measurement) all but one of those possibilities collapse. How does this happen? What mechanism is responsible for selecting one of those states over the rest? To date there is no answer. Despite this, von Neumann’s idea has been taken seriously because his approach allows for unique outcomes.The problem that von Neumann was trying to address is that the Schrödinger equation itself does not select single outcomes. It cannot explain why unique outcomes are observed. According to it, if a fuzzy mix of properties comes in (coded by the state vector), a fuzzy mix of properties comes out. To fix this, von Neumann conjured up the idea that the state vector jumps discontinuously (and randomly) to a single value. [xxiii] He suggested that unique outcomes occur because the state vector retains only the “component corresponding to the observed outcome while all components of the state vector associated with the other results are put to zero, hence the name reduction.” [xxiv]The fact that this reduction process is discontinuous makes it incompatible with general relativity. It is also irreversible, which makes it stand out as the only equation in all of physics that introduces time-asymmetry into the world. If we think that the problem of explaining uniqueness of outcome eclipses these problems, then we might be willing to take them in stride. But to make this trade worthwhile we need to have a good story for how state vector collapse occurs. We don’t. The absence of this explanation is referred to as the quantum measurement problem.Many people are surprised to discover that the quantum measurement problem still stands. It has become popular to explain state vector reduction (wave function collapse) by appealing to the observer effect, asserting that measurements of quantum systems cannot be made without affecting those systems, and that state vector reduction is somehow initiated by those measurements. [xxv] This may sound plausible, but it doesn’t work. Even if we ignore the fact that this ‘explanation’ doesn’t elucidate howa disturbance could initiate state vector reduction, this isn’t an allowed answer because “state vector reduction can take place even when the interactions play no role in the process.” [xxvi] This is illustrated by negative measurements or interaction free measurements in quantum mechanics.To explore this point, consider a source, S, that emits a particle with a spherical wave function, which means its values are independent of the direction in space. [xxvii] In other words, it emits photons in random directions, each direction having equal probability. Let’s surround the source by two detectors with perfect efficiency. The first detector D1should be set up to capture the particle emitted in almost all directions, except a small solid angle θ, and the second detector D2 should be set up to capture the particle if it goes through this solid angle (Figure 8).Figure 8 An interaction-free measurement When the wave packet describing the wave function of the particle signNowes the first detector, it may or may not be detected. (The probability of detection depends on the ratio of the subtended angles of the detectors.) If the particle is detected by D1 it disappears, which means that its state vector is projected onto a state containing no particle and an excited detector. In this case, the second detector D2will never record a particle. If the particle isn’t detected by D1 then D2 will detect the particle later. Therefore, the fact that the first detector has not recorded the particle implies a reduction of the wave function to its component contained within θ, implying that the second detector will always detect the particle later. In other words, the probability of detection by D2 has been greatly enhanced by a sort of “non-event” at D1. In short, the wave function has been reduced without any interaction between the particle and the first measurement apparatus.Franck Laloë notes that this illustrates that “the essence of quantum measurement is something much more subtle than the often invoked ‘unavoidable perturbations of the measurement apparatus’ (Heisenberg microscope, etc.).” [xxviii] If state vector reduction really takes place, then it takes place even when the interactions play no role in the process, which means that we are completely in the dark about how this reduction is initiated or how it unfolds. Why then is state vector reduction still taken seriously? Why would any thinking physicist uphold the claim that state vector reduction occurs, when there is no plausible story for how or why it occurs, and when the assertion that it does occur creates other monstrous problems that contradict central tenets of physics? The answer may be that generations of tradition have largely erased the fact that there is another way to solve the quantum measurement problem.Returning to the other option at hand, we note that if we assume that the state vector is a statistical ensemble, if we assume that the system does have a more exact state, then the interpretation of this thought experiment becomes straightforward; initially the particle has a well-defined direction of emission, and D2records only the fraction of the particles that were emitted in its direction.Standard quantum mechanics postulates that this well-defined direction of emission does not exist before any measurement. Assuming that there is something beneath the state vector, that a more accurate state exists, is tantamount to introducing additional variables to quantum mechanics. It takes a departure from tradition, but as T. S. Eliot said in The Sacred Wood, “tradition should be positively discouraged.” [xxix] The scientific heart must search for the best possible answer. It cannot flourish if it is constantly held back by tradition, nor can it allow itself to ignore valid options. Intellectual journeys are obliged to forge new paths.So instead of asking whether of not wave-particle duality is an illusion, perhaps we should ask whether wave-particle duality implies that the state vector is the most fundamental description of a quantum mechanical system, or if a deeper level description exists? That's an open question, and at the moment there are many possible answers — interpretations of quantum mechanics that are equally aligned with the empirical evidence. What's your answer?For more on this topic, and to discover how pilot-wave theory is elucidated by the assumption that the vacuum is a superfluid, see Einstein's Intuition, available in black and white softcover, full color softcover, full color hardcover, an iBook, and as an audiobook.[i] The discussion on interference and the double-slit experiment that follows is further developed by Brian Greene, (2004). The Fabric of the Cosmos: Space, Time and the Texture of Reality. New York: Knopf, pp. 84–84. Greene’s discussion was used as a general guide here.[ii] In order to show diffraction (a fuzzy border of light on the projected image) the slit must have a width that does not greatly exceed the wavelength of the color of the light that we have chosen.[iii] Light’s wave nature was first revealed in the mid-seventeenth century through experiments performed by the Italian scientist Francesco Maria Grimaldi, and was later expanded upon by experiments performed in 1803 by the physician and physicist Thomas Young. (1807). Interference of Light; Alan Lightman. A Sense Of The Mysterious. pp. 51–52, 71.[iv] Before the “planetary model” of the atom, physicists pictured the atom being a plum-shaped blob (the nucleus) with tiny protruding springs that each had an electron stuck to its end. When the atom absorbed energy it was thought that these electrons would jiggle (oscillate) on the ends of their springs. Consequently, any atom that was above its ground state of energy was understood to be an “excited atomic oscillator,” This depiction of the atom wasn’t overthrown until 1900. At that point in history the physical existence of atoms was still controversial. It was replaced by the planetary model, which in turn was replaced by the electron cloud model we use today—a model that was initiated in 1910 and was secured by 1930. Gary Zukav. The Dancing Wu Li Masters, pp. 49–50.[v] Electrons can be individually counted and you can individually place them on a drop of oil and measure their electric charge. Richard Feynman. (1988). QED, The Strange Theory of Light and Matter. Princeton University Press, p. 84.[vi] According to de Broglie’s doctoral thesis all matter has corresponding waves. The wavelength of the “matter waves” that “correspond” to matter depends upon the momentum of the particle. Specifically, , which falls into an important group of equations along with Planck’s equation ) and the ever famous . (λ, pronounced “lambda,” stands for wavelength, h is Planck’s constant, and pronounced ‘nu’ represents the frequency of a photon) From this equation we are told to expect that when we send a beam of electrons (something we might traditionally think of as a stream of particles) through tiny openings, like the spacing between atoms in a piece of nickel crystal, the beam will diffract, just like light diffracts. The only requirement here is that the spacing between the atoms of the material must be as small, or smaller, than the electron’s corresponding wavelength—just like the slits in our double-slit experiment. When we perform the experiment, diffraction and therefore interference, occurs exactly as wave mechanics predicts.[vii] Part of the problem here is that in keeping with our four-dimensional intuition we tend to assume a particle aspect in the double-slit experiment without accounting for nonlocality. By doing this we are technically violating Heisenberg’s uncertainty principle and missing the bigger picture.[viii] M. Born. (1926). Quantenmechanik der Stossvorgänge. Zeitschrift für Physik 38, 803–827; (1926). Zur Wellenmechanik der Stossvorgänge. Göttingen Nachrichten 146–160.[ix] Brian Greene. (2004), p. 91.[x] Albert Einstein quoted in Einstein by Walter Isaacson.[xi] Walter Isaacson. Einstein, pp. 96–97.[xii] Ibid.[xiii] Werner Heisenberg. The Physical Principles of the Quantum Theory, p. 20.[xiv] Masano Ozawa. (2003). Universally valid reformulation of the Heisenberg uncertainty principle on noise and disturbance in measurement. Physical Review A 67 (4), arXiv:quant-ph/0207121; Aya Furuta. (2012). One Thing Is Certain: Heisenberg’s Uncertainty Principle Is Not Dead. Scientific American.[xv] L. A. Rozema, A. Darabi, D. H. Mahler, A. Hayat, Y, Soudagar, & A. M. Steinberg. (2012). Violation of Heisenberg’s Measurement—Disturbance Relationship by Weak Measurements. Physical Review Letters 109 (10).[xvi] Steven Weinberg. Dreams Of A Final Theory, p. 74.[xvii] For a system of spinless particles with masses, the state vector is equivalent to a wave function, but for more complicated systems this is not the case. Nevertheless, conceptually they play the same role and are used in the same way in the theory, so that we do not need to make a distinction here. Franck Laloë. Do We Really Understand Quantum Mechanics?, p. 7.[xviii] Franck Laloë. Do We Really Understand Quantum Mechanics?, p. xxi.[xix] There are 6N dimensions in this phase space because there are N particles in the system and each particle comes with 6 data points (3 for its spatial position (x, y, z) and 3 for its velocity, which has x, y, zcomponents also).[xx] The space of states (complex vector space or Hilbert space) is linear, and therefore, conforms to the superposition principle. Any combination of two arbitrary state vectors and within the space of states is also a possible state for the system. Mathematically we write where & are arbitrary complex numbers.[xxi] Franck Laloë. Do We Really Understand Quantum Mechanics?, p. 19.[xxii] Chapter VI of J. von Neumann. (1932). Mathematische Grundlagen der Quantenmechanik, Springer, Berlin; (1955). Mathematical Foundations of Quantum Mechanics, Princeton University Press.[xxiii] It might be useful to challenge the logical validity of the claim that something can “cause a random occurrence.” By definition, causal relationships drive results, while “random” implies that there is no causal relationship. Deeper than this, I challenge the coherence of the idea that genuine random occurrences can happen. We cannot coherently claim that there are occurrences that are completely void of any causal relationship. To do so is to wisk away what we mean by “occurrences.” Every occurrence is intimately connected to the whole, and ignorance of what is driving a system is no reason to assume that it is randomly driven. Things cannot be randomly driven. Cause cannot be random.[xxiv] Franck Laloë. Do We Really Understand Quantum Mechanics?, p. 11.[xxv] Bohr preferred another point of view where state vector reduction is not used. D. Howard. (2004). Who invented the Copenhagen interpretation? A study in mythology. Philos. Sci. 71, 669–682.[xxvi] Franck Laloë. Do We Really Understand Quantum Mechanics?, p. 28.[xxvii] This example was inspired by section 2.4 of Franck Laloë’s book, Do We Really Understand Quantum Mechanics?, p. 27–31.[xxviii] Franck Laloë. Do We Really Understand Quantum Mechanics?, p. 28.[xxix] T. S. Eliot. (1921). The Sacred Wood. Tradition and the Individual Talent.
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