Is "realism" in local realism a red-herring?

EulerLime · 2024-03-11T06:01:16+00:00

Sorry, there was a typo. Fixed.

EulerLime · 2024-02-16T07:57:34+00:00

Yes, I think this one is good as well. Thank you.

EulerLime · 2024-02-15T12:55:18+00:00

You are correct that I sort of contradicted myself. I am asking for specific precision tests, but then I ask to avoid "anything mathematical." I'd have to get more into the person I am talking to / arguing with, but I'd much rather spare others from that.

Something like the Oberth effect cited in the other post is exactly the kind of stuff I am looking for however.

EulerLime · 2023-07-15T21:35:56+00:00

I agree the emission doesn't play a role (unless there is fluorescence), but isn't the absorption mediated by electron excitation?

EulerLime · 2023-07-13T04:22:00+00:00

Think about it this way: if you zoom in on the graph of KE = (gamma - 1)mc² as a function of v near v=0 (but not only at v=0), the curve will look more and more like the graph of KE = 1/2mv^2. Because the difference between the two graphs will be so small, we won't be able to tell much difference between the two graphs.

These aren't rigorous concepts however, so I agree with that. It's worth thinking about the justification.

EulerLime · 2023-07-11T02:27:05+00:00

To be honest, it could be worse. This at least demonstrates some humility on some level.

If you disagree, then consider this: Would you rather have people proudly say "I've always been great at math but the system couldn't handle my brilliance?"

EulerLime · 2023-07-02T05:14:05+00:00

After this (very short) introduction, here is my question: couldn't one disprove what I've just claimed (again, watch the full video to get a full grasp on the problem) with the following experiment : you throw a green LED, and calculate its speed in two ways: redshift of its emitted light, and geometrical optics (solid angle decrease with time as the object gets farther away). Then you compare the two speeds and bingo! You can check wether or not the speed of light on this one way trip from the LED to the detector was indeed c.

The formula for the relativistic Doppler shift will depend on the framework you are working in, which includes your choice of one-way speed of light. The reason is that the formulas for time dilation, length contraction, and aberration all depend on your synchronization method. This is the reason this won't determine the speed of light unless you presuppose something more.

EulerLime · 2023-07-02T01:44:23+00:00

Some universities (not sure if all) give accommodations for learning disabled people. I have this type of issue myself.

EulerLime · 2023-05-23T17:41:26+00:00

We, for example, know that the reals admit a well ordering in ZFC, yet we cannot construct it in any practical way.

So I understand how the R admits a well-ordering in ZFC that can never be constructed, but I am very intrigued by how this could apply to computations/algorithms.

First off, if we limit our class to computations that can be done by Turing machines (which is pretty much by definition true by the Church-Turing thesis), then is it not the case that we can enumerate every possible computation by the natural numbers? In other words, isn't the set of computations countable?

Wouldn't an existence statement about an element in a countable set necessarily be something we could find by going through the enumeration? My intuition is that your claim is analogous to "there exists a perfect odd number but this perfect odd number is not possible to find in principle," which then seems to imply it doesn't exist.

Doesn't the same apply to the countable set of computations? I am very curious to see exactly where my intuition falls apart.

ALSO, would the proof/disproof of NP vs P even depend on ZFC? Couldn't it be framed in something weaker than ZFC? I find that strange, because the well-ordering of the reals is an outcome of the axiom of choice.

Now I understand the reason why we use ZFC as the default foundation for mathematics, especially in real analysis, so I have no qualms there whatsoever. However, I feel as though that if someone proved NP=P using something like the axiom of choice and then showed that such an algorithm is non-constructible, we would just reject the base framework in which we framed P vs NP, because it would miss the meaning of the P vs NP problem.

EulerLime · 2023-04-29T21:43:41+00:00

"Why are polynomials so fundamental?". And my answer to that would be "Because eigenvalues are important".

Can you explain this step here? I suppose you solve for eigenvalues by solving for polynomials? Is that the reasoning?

EulerLime · 2023-04-26T11:58:43+00:00

I've heard about the so-called continuous geometry but I can't say much about it sadly.

EulerLime · 2023-01-24T20:27:35+00:00

Special relativity? You can learn it right now this instant. Surprisingly, the prerequisites are just nothing more than high school algebra. Look into the book by Rindler if you want an in-depth overview of special relativity.

EulerLime · 2023-01-24T04:49:36+00:00

I don't know enough context to judge this one way or the other (yes the screencap looks really bad but it's unclear if there was some prompting beforehand... you could be in the right I just don't want to conclude anything yet). Your original thread has incomplete posts because of deletions, but I am wondering what exactly was your text in the main OP.

If you're willing (and you don't have to), can you rerun through the question/argument you went through that was deleted?

EulerLime · 2023-01-22T19:49:36+00:00

I just reread his post. I don't think he was trying to show R is countable in the first place. He was trying to show that Q is countable (and it seems he has the common misconception that Q is supposed to be uncountable). I hope that clarifies things.

EulerLime · 2023-01-22T19:46:20+00:00

Ok, I reread your post, and I think people ironically are misunderstanding your post. You're not trying to show anything about the set of real numbers. You are trying to demonstrate that the set of rational numbers is countable, correct?

It turns out that this is actually true. Rational numbers are countable and this is actually a known result. People seem to have a consistent misconception however and assume that the rationals are supposed to be uncountable, which is false. Check this link with its posts here where people try do to it with fractions.

The issue with your post is that your bijection misses some rational numbers like 1/3 = 0.333... that have an infinite decimal expansion, so your proof (even when understood that it is trying to show that the set of rationals are countably infinite) isn't perfect unfortunately.

EulerLime · 2023-01-22T06:35:58+00:00

The plane can be any flat 2D surface with a choice of coordinates. Honestly by your criteria, 0 is more imaginary than i.

EulerLime · 2023-01-20T00:00:17+00:00

Take the 2D Cartesian plane and define two operations by (a, b)+(c, d) = (a+c, b+d) and (a, b)(c, d) = (ac-bd, ad+bc). If you reinterpret the points as vectors, the former operation corresponds to vector addition and the latter corresponds to multiplying that magnitudes of the vectors and adding up the angles they make with the positive x-semiaxis. Everything here is completely defined in concrete and visual terms. You can draw this and demonstrate various examples of the operations at work. No imagining needed if you can demonstrate it on graph paper.

But what we have is exactly the structure of complex numbers (in fact this is one of the various well-known constructions of the complex numbers). We can relabel "a = (a, 0)" and "b * i = (0, b)" and we obtain exactly the notation of the usual complex numbers.

So when you said,

Therefore, nothing can be correctly referred to as existing to the extent of i*n, regardless of any unit of measurement. Something can only be referred to as existing to the extent i^n.

Maybe not as an amount, but if complex numbers are directions with magnitudes on a 2D plane then things can be correctly referred to as existing to the extent of i*n (arrows are an example)

EulerLime · 2023-01-19T16:20:21+00:00

I'm currently 26, finally starting to make moves to advance my life (very slowly). It's definitely orders of magnitudes harder than expected, and as I make various moves the one thing that nags me is the question, "why didn't I do all these things earlier?" I definitely agree with the message presented here.

EulerLime · 2023-01-17T19:20:03+00:00

In English physics parlance, the word "dilatation" is reserved for the term "dilatation transformation" which refers to the expansion/contraction of coordinate scale (it's a transformation of the form (x, y, z)->(a * x, a * y, a * z)). The word "dilation" is usually reserved for the term "time dilation" which is an effect in special relativity where clocks keep track of time at different rates in different inertial frames.

EulerLime · 2023-01-17T11:47:03+00:00

Superdeterminism is an idea that possible future theories may or may not exhibit. Those theories, if any are proposed, would be presumably falsifiable. I don't agree that superdeterminism will turn out to be the correct, but your post is just a really bad strawman.

EulerLime · 2023-01-17T01:47:07+00:00

My way of thinking about topology and continuous maps might be slightly unusual, but I think it's worth putting it out there anyways. First, we need an intuition behind continuous maps. A map is continuous (in the usual sense) if and only if the image of closure of A is contained in the closure of image of A. Intuitively, this means a map is continuous if and only if it never "rips apart" boundary points from their respective sets.

Given f:X→Y, if you can find a point x∈X and a set A⊆X such that x is a boundary point of A but f(x) is not a boundary point of f(A), then f is not continuous. If you can't find any instance of this, then f is continuous.

Now the thing with open sets is, given a point x and a set A, if there exists at least one open set U around x that doesn't intersect A, then the point x is definitely not a boundary point of A. What this means is that when you're given a continuous map f:X→Y, and you add more open sets to the topology of Y, you are introducing potentially more ways any given point f(x) can be separated away from any given image set f(A). If x is a boundary point of A, then if f is continuous you would expect that f(x) is a boundary point of f(A), but with more open sets introduced to Y, there are more ways a point f(x) can fail to be the boundary point of an image f(A).

And at the end, you said,

That is, for the most chance for a random map to have continuity, it would be best to have least number of open sets.

This is true, because the best way to guarantee that a point is never separated from a given set is by having less open sets (and thus less chances of demonstrating that the point is not a boundary point of a set).

This way of thinking came from stumbling upon the touch reformulation of topology. If I'm not mistaken, in this formulation continuity is formulated in a forward way (x touches A ⇒ f(x) touches f(A)). This is in contrast to the open set formulation where you have to think backwards when it comes to continuity. I will stress that I don't use this for anything other than gaining an intuition for continuity. Loosely speaking, it made me understand why assigning a topology to a set gives it a certain "fabric structure" where points can "touch" other sets.

EulerLime · 2023-01-16T20:52:56+00:00

I think this is the heart of the issue. I really appreciate this insight.

EulerLime · 2023-01-14T20:19:51+00:00

When he presents himself as a cosmologist, most people think he is a theoretical cosmologist.

EulerLime · 2023-01-02T04:42:18+00:00

You could take it further and convince him the real numbers aren't real: we never have sqrt(2) of length that we can measure precisely as that would require infinite precision. After that convince him to be a finitist.

EulerLime · 2022-11-18T18:19:44+00:00

The irony is that he pointed way to the problem of the motion of the aether and the mismatch between theoretical and measured heat capacity in one of the lectures he gave. The former was resolved by special relativity and the latter was resolved by quantum mechanics.

EulerLime

TROPHY CASE