When I read about past events in the universe (i.e. big bang, formation of the sun and planets, etc) future events (i.e. sun becoming a red giant) and distant objects (black holes, nebulas, galaxies, etc), it appears to me that a big assumption is always made:  The laws of physics observed from earth today are the same throughout the universe, and throughout time.  My question is: do we have any evidence that supports this assumption? Or do we make this assumption simply  because we have never seen evidence to the contrary?
Hubble's constant $a(t)$ appears to be changing over time. The fine stucture constant $\alpha$, like many others in QFT, is a running constant that varies, proportional to energy being used to measure it. Therefore, it could be agued that all running constants have 'evolved' over time as the Universe has expanded and cooled. Both the local and global curvature of the Universe changes over time implying that so too does the numerical value of $\pi$. All these things are however constants (well, let's say parameters since they are not really 'constant'.)   In  with astronomer Sir Fred Hoyle, Feynman said "what today, do we not consider to be part of physics, that may ultimately become part of physics?" He then goes on to say "..it's interesting that in many other sciences there's a historical question, like in geology - the question how did the Earth evolve into the present condition? In biology - how did the various species evolve to get to be the way they are? But the one field that hasn't admitted any evolutionary question - is physics."  So have the laws of physics remained form-invariant over the liftetime of the Universe? Does the recent understanding of the aforementioned not-so-constant constants somehow filter into the actual form of the equations being used? Has advances in astronomical observations, enabling us to peer back in time as far back as the CMB, given us any evidence to suggest that the laws of nature have evolved? If Feynman thinks that "It might turn out that they're not the same all the time and that there is a historical, evolutionary question." then this is surely a question worth asking.  NB/ To be clear: this is a question concerning purely physics, whether the equations therein change as the Universe ages, and whether there is any observational evidence for this. It is not intended as an oportunity for a philosophical discussion.
Cardinality of a set A is strictly less than the cardinality of the power set of A Error: invalid environment block. Press any key to continue...   The error message appears immediately after the boot screen on purple background. Ubuntu 12.04.1 LTS. Programmatically open new pages on Tabs Button that triggers modal Lenovo Legion Y720 laptop Keyboard backlight I just moved from Windows to Ubuntu, but I cannot get the keyboard backlight to work at all. On Windows there was a specific program for controlling the backlight. I have searched for days now without luck. Anyone got a solution?  I am using Ubuntu 18.04 What is the difference between Shrink Database and File? DBCC ShrinkDatabase() DBCC ShrinkFile()    Do I need to run both DBCC commands in order to shrink the database? What is the difference between these two above? return statement vs exit() in main() Should I use exit() or just return statements in main()? Personally I favor the return statements because I feel it's like reading any other function and the flow control when I'm reading the code is smooth (in my opinion). And even if I want to refactor the main() function, having return seems like a better choice than exit().  Does exit() do anything special that return doesn't? How to set up beamer to grey out past items but hide future items? I know about beamer's  feature \setbeamercovered{invisible} and \setbeamercovered{transparent} to hide or grey out upcoming item's . But is there some way to have past items greyed (transparent) and future items hidden (invisible), so that only the current item is black/highlighted? And the best would be if on or 1 slide after the last all the item's could be visible highlighted. Something like this:   [grey] past 1 [grey] past 2 current [hidden] future 1 [hidden] future 2 [hidden] future 3   Is there any easy way of doing this? I've shown the existence of unique square roots of all positive rational numbers, so now I want to prove that the square root is monotone:   $0&lt;a&lt;b$ if and only if $\sqrt{a} &lt; \sqrt{b}$ When app is moved to SD card, where is the app data stored on SD card? Is there a way to get the raw SQL string executed when calling PDOStatement::execute() on a prepared statement? For debugging purposes this would be extremely useful. Deleting comments under posts in the mod queue should be easier Ever since mods gained the ability to undelete comments, deleting them has become easier as the confirmation dialog was removed.  However, this is not the case in the mod queue &mdash; I still get a confirmation dialog for each comment I want to delete in the queue under a custom-flagged post (single-comment flags can be deleted just fine). And since this is the place from where I delete comments the most, it can be annoying.  In addition, the "purge comments" button, when invoked from the queue, refreshes it, so I have to scroll back down, remember which post I just purged, and mark the flag as helpful. Usually not a big issue but if there are multiple "obsolete comments" flags, then it can get confusing.  Could the workflow for comment thread moderation from within the queue be improved? Ideally, make comment deletion work like everywhere else on the site, and make the purge button AJAX-based like the comment deletes. Why is it possible to answer a question twice? Casting two cantrips, both modified by metamagic? Can you cast one cantrip, modifying it with "Twinned Spell" (Fire Bolt) to target 2 creatures, and then cast another cantrip as a Bonus Action (Fire Bolt), using "Quickened Spell" to target one of the previous creatures or another creature? What does 1x1 convolution mean in a neural network? I am currently doing the Udacity Deep Learning Tutorial. In Lesson 3, they talk about a 1x1 convolution. This 1x1 convolution is used in Google Inception Module. I'm having trouble understanding what is a 1x1 convolution.  I have also seen  by Yann Lecun.  Could someone kindly explain this to me? Matlab Recursion Loop Explode string into array with no empty elements? PHP's explode function returns an array of strings split on some provided substring. It will return empty strings when there are leading, trailing, or consecutive delimiters, like this: var_dump(explode('/', '1/2//3/')); array(5) {   [0]=&gt;   string(1) &quot;1&quot;   [1]=&gt;   string(1) &quot;2&quot;   [2]=&gt;   string(0) &quot;&quot;   [3]=&gt;   string(1) &quot;3&quot;   [4]=&gt;   string(0) &quot;&quot; }  Is there some different function or option or anything that would return everything except the empty strings? var_dump(different_explode('/', '1/2//3/')); array(3) {   [0]=&gt;   string(1) &quot;1&quot;   [1]=&gt;   string(1) &quot;2&quot;   [2]=&gt;   string(1) &quot;3&quot; } Show that if the smallest prime factor $p$ of the positive integer $n$ exceeds $\sqrt[3]{n}$, then $\frac{n}{p}$ must be prime or 1.  I'm stuck trying to prove this. I tried this using contradiction, but I haven't been able to prove it.  My approach:  Let $p$ be the smallest prime factor of the positive integer $n$.  Let $p &gt; \sqrt[3]{n}$  Then we must show that $\frac{n}{p}$ is either a prime number or 1.  We know that $n = pe$ for some $e \in \mathbb{Z}$.  Thus, $\frac{n}{p} = e$  We also know that $p$ > $\sqrt[3]{n}$, so $p^3 &gt; n$, and $p^2 &gt; \frac{n}{p}$  So, assume $\frac{n}{p} = e$ is not prime nor 1, meaning it's a composite number. Let's try to get a contradiction.  If $\frac{n}{p}$ is composite, then $\exists a,b \neq 1: \frac{n}{p} = ab $  Now, here's where I get stuck. What can I do with this info? $\frac{n}{p} = ab $ and $p^2 &gt; \frac{n}{p}$. ASP.NET MVC Relative Paths In my applications, I often have to use relative paths. For example, when I reference JQuery, I usually do so like this:  &lt;script type="text/javascript" src="../Scripts/jquery-1.2.6.js"&gt;&lt;/script&gt;   Now that I'm making the transition to MVC, I need to account for the different paths a page might have, relative to the root. This was of course an issue with URL rewriting in the past, but I managed to work around it by using consistent paths.  I'm aware that the standard solution is to use absolute paths such as:  &lt;script type="text/javascript" src="/Scripts/jquery-1.2.6.js"&gt;&lt;/script&gt;   but this will not work for me as during the development cycle, I have to deploy to a test machine on which the app will run in a virtual directory. Root relative paths don't work when the root changes. Also, for maintenance reasons, I cannot simply change out all the paths for the duration of deploying the test - that would be a nightmare in itself.  So what's the best solution?  Edit:  Since this question is still receiving views and answers, I thought it might be prudent to update it to note that as of Razor V2, support for root-relative urls is baked in, so you can use   &lt;img src="~/Content/MyImage.jpg"&gt;   without any server-side syntax, and the view engine automatically replaces ~/ with whatever the current site root is. Strictly diagonally dominant matrices are non singular