Ghideon

Trying to provide a hint*, assuming I understand the problem: -It may help to look at different parts of the DFA in isolation and what each part contribute. -You can try to apply one specific example to the DFA and check want comes out. Let's try the second case using "abba". As "a" is entered as input to the DFA, the upper path will be followed. Can you figure out what happens for the next character in "abba", the first "b"? Do we progress to a new state or stay in the same state? *) no complete answer since this is homework section

Here is a simplified picture that may help: A white train T moves relative to points A and B The points A and B are not moving relative one another. The train T moves from left to right when seen from a position at point A. An Observer on the other side of the train (at location B) will see the train going from right to left. Basic observations: 1: There is one train. 2: The number of observers does not affect the number of trains. 3: The concept of left and right depends on point of view. Hopefully the above simplified example may help you form the correct questions or identify misunderstandings.

There is some frame of reference S where a 100m long train (proper length) will have the length 1m according to special relativity. If the question "world lines are 1 meter apart" is physically meaningful, can you explain how?

And In the last question, do you mean a 100m long train (proper length), a 1m long train (proper length), special relativity length contraction of 100m to 1m (measured in some frame of reference)? Or something else? Proper length or rest length is the length of an object in the object's rest frame. (https://en.wikipedia.org/wiki/Proper_length)

I disagree with the conclusion. The currently used system of units allows us to design space probes and rowers that works predictably in micro gravity and on other planets. It sounds unnecessary complicated, from an engineering perspective, to plan and execute such missions if the units of measure depends on location. Side note: confusion between metric and imperial units has caused at least one failure already; the Mars Climate Orbiter: Source: https://web.archive.org/web/20010920052120/http://sunnyday.mit.edu/accidents/MCO_report.pdf

A specific observer can't move relative themselves; one observer is always in one inertial frame*. So the observer will make observations, consistent with relativity theories, in that single frame. That means the observer will observer one and only one set of x and t coordinates (as described by @md65536). *) Multiple observers may share a single frame and any observer may change frame but as far as I know no observer can be simultaneously in two different frames.

Any comments on my first response in this thread? From the viewpoint (inertial frame) of a muon traveling through the earth's atmosphere the length contraction effect of special relativity allows the muon to penetrate and reach earth. In the muon frame its lifetime is unaffected, but the length contraction causes distances through the atmosphere and Earth to be far shorter than these distances in the Earth rest-frame. The above is not an illusion; the distance through the atmosphere is, was, and will be different in different inertial frames and it has physical effects. (above text is based on https://en.wikipedia.org/wiki/Muon)

Note that in the double slit experiment interference pattern emerges also when photons* are allowed to build up one by one. Your explanations seems to rely on the particle being charged, how do you explain the fact that we observe interference of individual uncharged particles? *) or other particles with no net charge

Additional dimensions are not part of established relativity theories. AFAIK the models does not try to answer your question. For an observer within our universe the relative velocity between the observer and the train together with Lorentz transformation will get you the answer. Relativistic effects are confirmed in experiments, I don not think illusion is a proper label. Here is an example of time dilation / length contraction: https://en.wikipedia.org/wiki/Muon

A link to the article could be good. edit: Is this the article? https://www.americanscientist.org/article/the-curse-of-emc2 (Can't read it, requires a login)

Why? What is the purpose? Note that [math]q^2-\frac{N q^2+q}{N}=-q/N[/math]

The error indicates that the code is missing an import statement for the class (or package) that defines SimpleRegression. For more information about Java import ser for instance : https://www.w3schools.com/java/ref_keyword_import.asp

Here is an attempt, assuming I interpret the requirements correctly: [math]Y=\frac{X}{X+A}[/math] where X is "initial total balance" (or the sum of all users' initial number of units) and A is the amount added (newUnits in the example above). The new allocation for a user is calculated as Y∗U where U is the number of units the user has. For one user (A in the example above) that means using the updated number of units. Trying the example: X=100, A=20 -> [math]Y=\frac{X}{X+A}=\frac{100}{100+20}=\frac{5}{6}[/math] A: [math]\frac{30*5}{6}=25[/math] B : [math]\frac{20*5}{6}\approx 16.67[/math] C : [math]\frac{30*5}{6}=25[/math] D : [math]\frac{40*5}{6}\approx 33.33[/math]

@Trurl there are some Latex errors in your message, it is not readable. Here is a screenshot of how it looks like:

How did you get the number 3? From your formulas or by some other method? I do not understand. If that is due to my lack of abilities or lack of valid explanations, I'll let others judge. And I am still waiting for a connection to RSA encryption and prime factorisation of large integers.

I am looking forward to a connection to RSA encryption and prime factorisation of large integers. Ok. I'll try two examples: 8633, 8637. Both are semi primes. NSolve [( x^4/((8637)^2 + x)) == 1] x≈-92.935 x≈92.935 NSolve [( x^4/((8633)^2 + x)) == 1] x≈-92.914 x≈92.914 @Trurl Is this helpful for someone looking for the prime factors of the numbers 8633 and 8637? If so, how?

Unless you want a general list as already provided above some context would be good to sort out what possibilities we have. Example: we can have face recognition instead of a password to open a smartphone. An X.509 certificate may be useful instead of a password in a server-to-server scenario. The opposite, unlocking a smart phone with an X.509 certificate or have servers identify themselves via face recognition may not be a good idea at all.

As far as I know that is an unsolved problem at this time*. *) Assuming the context is computer science where a one-way function is a function that is easy to compute on every input, but "hard" to invert given the image of a random input. https://en.wikipedia.org/wiki/One-way_function;

Interesting link, thanks! Is the above a speculation of yours or by the authors of the article? I did a quick read of the Astrophysical Journal Letters: from https://iopscience.iop.org/article/10.3847/2041-8213/ab5b9f, linked from the phys.org source.

My personal (and rather naive) answer: We do not know if the universe* is infinite or finite and if there are infinite or finite number of particles. Mathematics contain tools and concepts usable for both cases. *) The observable universe is finite and contains a finite amount of matter.

Ok. Very old phones have no camera. So a newer phone may be required to solve your issue. (You may get more helpful responses if you provide more context)

As far as I know the constant G is required in General Relativity to get time dilation and other predictions in the first place. Saying "G in the GRT equation must be a variable whose value is inversely proportional to the time dilation" sounds like a contradiction. Which means that G is constant.

Ok! Thanks for clarifying. Do you mean that black holes as described by established theories do not exist? Is your claim that General Relativity is wrong?

I know about the gravitational redshift but I do not see the connection to a change in size. Your statements seem to imply that objects very near the event horizon of a black hole will be extremely long according to an observer far from the black hole. When the redshift is extreme the change in length will be extreme. Is this a correct interpretation of your opening post?

How come the tree is taller when measured by a remote observer, higher up in the gravity well ? How is that measurement performed? I'm curious, I can't remember reading about such an effect (but my GR knowledge is very limited).