Special relativity time dilation messing with my head Say we have the earth and a person on it and an astronaut travelling away from the earth in a spaceship in a straight line and then coming back in a straight line at the same speed.   The person on the earth measures the time between when the astronaut leaves and when he comes back as 1 year. This is a proper time since the observer has not moved in his frame of reference. Thus according to the relation $t = \gamma t_o$ the astronaut must have experienced a longer time.   The person on the spaceship measures the time from takeoff to landing as 1 year. Since he's standing at the same point in his frame of reference this is a proper time. Thus according to the relation $t = \gamma t_o$ the person on earth must have experienced a longer time.   The above is contradictory. Either the astronaut experiences a longer time or the person on earth does. The issue is that either the astronaut is thought to be moving relative to the earth or the earth is thought to be moving relative to the astronaut. What's the explanation? Can anyone help me understand?  Okay. I’ve read through the below answers, as well as watched a few videos and the Wikipedia page on it, however, i don’t see any of them explaining it. They claim that the acceleration solves the issue, however, don’t we arrive at the same problem? In the earth point of view the astronaut is rotating, but you might as well see the earth as rotating in the astronauts view. In other words, same problem.
How is the classical twin paradox resolved? I read a lot about the classical twin paradox recently. What confuses me is that some authors claim that it can be resolved within , others say that you need . Now, what is true (and why)?
Can you block installers from making desktop shortcuts? I've been keeping my desktop totally free from shortcuts. I'd rather not have to take action to do so. In the DC Comics Universe, What Happens to Earthlings Under a Red Sun? Is it possible to use Matcap materials as an actual material for a model so that I can render with it? There are certain parts that I want to apply specific Matcaps textures to but I want to actually use them to render and not just for sculpting purposes.  Is this at all do-able? Is there a way to set my current location manually on Windows 8? Is there a way to set my current location manually on Windows 8? I don't have a GPS module, but the device is always located at the same place. The automatic detection via network sets a place 200 kilometers from here.  I searched for a setting that allows me to set the location by hand, but I didn't find one. I have a question about XTP_CHECKPOINT.  I'm using SQL Server 2014. I have a database that is in SIMPLE recovery model mode. It is also being replicated.  There are no open transactions. I've run DBCC OPENTRAN and it returns:     "No active open transactions."   But I keep getting this message whenever I try to create or drop a table or delete data: (I've replaced my actual database name with the word database_name)     "The transaction log for database 'database_name' is full due to 'XTP_CHECKPOINT'"     Does anyone know why this might be happening, and, more importantly, how can I make it stop?  And yes, the database really is in SIMPLE recovery model mode. i.e. The transaction log should truncate automatically.  Incidentally, another database that I have in full recovery mode did the same thing, started returning the same error:     The transaction log for database 'database_name' is full due to 'XTP_CHECKPOINT'   I tried to change the log growth settings to unlimited growth, but it wouldn't let me, returning the same error.  I can reproduce the problem without any XTP stuff at all, except for just the filegroup. Here's how: Is there any program to provide a consistent interface across multiple archive types? At the moment, if I download a compressed file, it could be any of a .tar.gz archive, a tar.bz2 arhive, a .zip archive or a .gz archive. And each time I do so, I have to remember what the command line options for that program are.  Is there any CLI program where I can just go:  undocompression somefile.??  and let it figure out what format the archive is in? (overly long name used to avoid conflicting with any real program) What does it mean for two objects to "touch"? If you've ever been annoyingly poked by a geek, you might be familiar with the semi-nerdy obnoxious response of      "I'm not actually touching you! The electrons in the atoms of my   skin are just getting really close to yours!"   Expanding on this a little bit, it seems the obnoxious geek is right. After all, consider Zeno's paradox. Every time you try to touch two objects together, you have to get them halfway there, then quarter-way, etc. In other words, there's always a infinitesimal distance in between the two objects.   Atoms don't "touch" each other; even the protons and neutrons in the nucleus of an atom aren't "touching" each other.  So what does it mean for two objects to touch each other?   Are atoms that join to form a molecule "touching"? I suppose the atoms are touching, because their is some overlap, but the subatomic particles are just whizzing around avoiding each other. If this is the case, should "touching" just be defined relative to some context? I.e, if I touch your hand, our hands are touching, but unless you pick up some of my DNA, the molecules in our hands aren't touching? And since the molecules aren't changing, the atoms aren't touching either?  Is there really no such thing as "touching"? Converting MultiLinestring to Linestring with PostGIS I have a multiline string and want to convert it to a linestring in order to use some functions that only work with linestrings. I used ST_Dump() and got a collection of my geometries. If I merge them back together, I still get the multilinestring. Should I get the Npoints and combine them together or something, in order to end up with a simple linestring? ST_LineMerge() also does not work on my multilinestring, it returns the same. my example,  MULTILINESTRING((-3.16420835153456 55.9269166007097,-3.164222 55.926918),(-3.1642070167833 55.9269296196706,-3.16421351659546 55.9268662214904),(-3.16421351659546 55.9268662214904,-3.16421636372824 55.9268384509897),(-3.16421636372824 55.9268384509897,-3.16422182573761 55.9267851753802),(-3.16422182573761 55.9267851753802,-3.16422870102352 55.926718114886),(-3.16422870102352 55.926718114886,-3.16423309121073 55.926675293667),(-3.16423309121073 55.926675293667,-3.16423565148822 55.9266503211093),(-3.16423565148822 55.9266503211093,-3.16424103159897 55.9265978443265),(-3.16424103159897 55.9265978443265,-3.16424680776317 55.9265415044985),(-3.16424680776317 55.9265415044985,-3.16425267254583 55.9264843002995),(-3.16425267254583 55.9264843002995,-3.16425541048045 55.9264575949012),(-3.16425541048045 55.9264575949012,-3.16426111146586 55.9264019883556),(-3.16426111146586 55.9264019883556,-3.1642667032531 55.9263474469124),(-3.1642667032531 55.9263474469124,-3.16426957768543 55.9263194101362),(-3.16426957768543 55.9263194101362,-3.16427488261739 55.9262676666359),(-3.16427488261739 55.9262676666359,-3.16428009893088 55.9262167875066),(-3.16428009893088 55.9262167875066,-3.164282741107 55.9261910161221),(-3.1642875546472 55.9261440655823,-3.164282741107 55.9261910161221),(-3.1642875546472 55.9261440655823,-3.16429466890915 55.9260746741522),(-3.16429466890915 55.9260746741522,-3.16430092974527 55.9260136069079),(-3.16430092974527 55.9260136069079,-3.16430822838418 55.9259424170929),(-3.16430822838418 55.9259424170929,-3.16431547242401 55.925871759829),(-3.16431547242401 55.925871759829,-3.16431448732505 55.9258328901507),(-3.16431770120536 55.9257327846001,-3.16431547242401 55.925871759829),(-3.164339 55.925777,-3.16431770120536 55.9257327846001)) How do I get the SQLSRV extension to work with PHP, since MSSQL is deprecated? Did spacetime start with the Big Bang?  I mean, was there any presence of this spacetime we are experiencing now before big bang? And could there be a presence/existence of any other space-time before the big bang? Is it correct to say "I kindly request you to..."? Isn't kindness already implied when you say "I request you to..."?  When I say "I humbly request you to...", the word humbly helps me to label the state of my behavior during the request.  On the other hand, what value does the word kindly add to the request? Normal distribution tail probability inequality I am trying to show that $$P(X&gt;t)\leq \frac{1}{2}e^\frac{-t^2}{2}$$ for $t&gt;0$ where $X$ is a standard normal random variable.  Perhaps this is simple.  I have been starting with  $$ \int_{t}^{\infty} \frac{1}{\sqrt{2\pi}} e^\frac{-x^2}{2}dx \leq \int_{t}^{\infty}\frac{x}{t}\frac{1}{\sqrt{2\pi}}e^\frac{-x^2}{2}dx = \frac{1}{t\sqrt{2\pi}}e^\frac{-t^2}{2}$$  but this is not what I want...I am looking for a much stronger inequality.   Any help in the direction of getting the $1/2$? Why are lamps and mesh lights not illuminating anything? How do you properly use namespaces in C++? I come from a Java background, where packages are used, not namespaces. I'm used to putting classes that work together to form a complete object into packages, and then reusing them later from that package. But now I'm working in C++.  How do you use namespaces in C++? Do you create a single namespace for the entire application, or do you create namespaces for the major components? If so, how do you create objects from classes in other namespaces? GCSE: Find the number of person that will go to a party How can angular velocity be constant even when there is a torque by friction? A cylinder at rest lying on a rough ground is given an impulse which imparts a translational velocity (no angular velocity) to it. The question goes ahead with finding time after which rolling starts etc. etc.  But I have another question: The friction from the ground will decrease the translational velocity but increase the angular velocity (as the torque of friction will be in the direction of rolling). After some time, the translational velocity will become equal to angular velocity and hence pure rolling will start.  After this time work done by friction will be 0 as the point of contact is not moving and hence translational velocity will be constant. Now my doubt is that, when translational velocity is constant, it implies angular velocity will also be constant (as translational velocity is a multiple of angular velocity). But the torque from friction (about the centre of mass) will not be zero which means angular velocity will not be constant. In some book where there was the same problem it was written friction will vanish. How can friction vanish? How can anguluar velocity be constant even when there is a torque by friction? Now let set $A$ be arbitrary. So set $A$ exists. Using axiom of pairing $\{A\}$ exists. And then using axiom of regularity, we can argue that $A \notin A$. So, there is some $x$ such that $x \notin A$. Is this a valid proof ? Thanks Why does my front derailleur not work when it is cold? When it is warm outside my front derailleur works just fine. But when it gets colder (40F) the lever on the handle bar does not catch and I can move it without any resistance the whole way without the derailleur shifting.  Update: The wire is not moving and the shifter is a Shimano Deore.  Any idea what can cause that and how to fix it? Combination with repetitions. Coding for an ordered covariate I am performing ordinal regression, I have 5 response categories and several predictors both continuous and categorical. I would like to add a predictor which is categorical but ordered (1, 2, 3, 4). I don't think it would be appropriate to apply the usual dummy coding for unordered categorical predictors, but when I searched for how to code this I did not find much information.  In  "linear coding" or "assuming linearity of the predictor effect" is mentioned, but without further details.  Does it mean I just use my ordered values as they are, i.e. use them as a continuous variable?