Ghideon

Can you add some detail? What is the speculation?

When tossing a fair coin n times: the difference between number of heads and number of tails approaches infinity: [math] \lim_{n \rightarrow \infty } |h-t| \rightarrow \infty [/math] You claim the above to be incorrect, can you provide your alternate version? Please use math symbols. Your description is vague, can you formulate your claims in a more formal way? The math of gamblers ruin says theorem states that the game always ends when players start with a limited amount of coins. The game cannot go on forever with limited amount of pennies. But if you want the game to have the possibility to go on forever; change the game so players start with an unlimited amount of pennies. The equation above still tells you what happens. My interpretation is that you claim: [math] \lim_{n \rightarrow \infty } |h-t| =0 [/math] where n=number of tosses of a fair coin, h=number of heads, t= number of tails But the above equation is not true. The amount of heads and tails will not balance. It will deviate as I pointed out earlier.

Can you provide a mathematic reason why you believe that? You seem to claim that gamblers ruin theorem is not correct. Another way of stating what I said is: http://mathworld.wolfram.com/GamblersRuin.html That means that no matter how many pennies the players may start with, eventually one of the players will have all the pennies.

Did you understand the difference between the two equations I posted? Which one of them do you claim to be incorrect?

Show how it is false then. This could be part of the misunderstanding?

I do not get the above. "The closer and closer they would get to the same amount of them being heads or tails." That sounds like the opposite of what is known about games and probabilities*. The more times you toss a fair coin the larger the probability that there will be a large difference between number of heads and tails. Here is an attempt at using mathematic symbols** for my statement. When tossing n times: the limit for number of heads divided by number of tails is 1. [math] \lim_{n \rightarrow \infty } \big(\frac{h}{t}\big) = 1 [/math] When tossing n times: the difference between number of heads and number of tails approaches infinity is unbounded. (edit, got some help from Strange) [math] \lim_{n \rightarrow \infty } | h-t | \rightarrow \infty [/math] I remember this being taught in connection to Gamblers Ruin Theorem https://en.wikipedia.org/wiki/Gambler's_ruin#Fair_coin_flipping. *) First occurring in "On Reasoning in Games of Chance", 1657? **) Not exactly sure if "equals infinity" is the correct way to write what I intend to say.

Thanks for clarification. You seem to argue that the probability of exactly 1/2 of many and approximately 50% of many should be the same? It is not. For a large number of coin tosses there is actually a very small chance that there is exactly 1/2 heads and 1/2 tails. The only time it is probable to throw identical number of heads and tails is when the process is not fair or random. If I did a lot of tries and got 1/2 heads each time I would be suspicious. Example: Throw the coin 1000000000 times. What is the probability to throw exactly 1/2 of 1000000000 heads? Close to zero. What is the probability of throwing about 50% of them heads? Close to 1. And what is the probability of throwing heads the next time? It's 1/2

First comment, your paper says That does not sound correct. It can only be approximately valid for small masses moving in the gravitational field of a large mass. Example; a small masses will accelerate towards earth at 1g. But replace the small mass with a large mass, such as Jupiter. I do not think the result will be that Jupiter accelerates towards earth at 1g.

You might want to try the quote function in the sandbox

Thanks for the clarification! I suspected that expansion of universe was intended, that's why I stubbornly kept asking. The words have similar meaning over here as well, care must be taken so the correct physical concept is referenced. I'll read your proposed idea again using expansion wherever inflation is stated.

But if you stand on the surface of a large ball and you are not allowed to jump or dig, where can you go? To your local left, right, back, forward. Two dimensions, not three.

I'll try a logical explanation with more detail without referring to math of specific laws of physics this time: Let's say two hypothetical devices are working perpetually* as a unit without external energy source. Perpetual motion device A feeds energy (1) into device B and then device B feeds energy (2) to device A. Since no external energy is added and operation is perpetual there is no internal energy wasted; efficiency is 100%. Device A runs from the energy provided by B and B runs from the energy provided by A. Hence, over time, A must supply B with the same amount of energy that A would require to operate in isolation. And B must provide A with the same amount of energy B would require to run in isolation. So the result is that the only way the device A and B could work as a 100% efficiency perpetual motion device together is if they could do so in isolation. A and B are perpetual devices on their own or the device (A+B) is not a perpetual device. In other words you can not build a perpetual motion device unless you have a set of perpetual motion devices. This does of course not alter the fact that perpetual motion machines is not possible. It is just a way of showing how OPs setup is not working in a general case. (I answered from phone earlier and was unable to use an image. This is pretty much same as @Janus but I had started drawing already so posting probably does not harm.) *) Not possible! Only used to setup the explanation.

No, transparency of everyday objects such as fan blades is not affected by velocity relative an observer I think it can be explained like this: Lets say that the fan blades cover 50% of the circular area of the fan. 50% is openings between blades. Start the fan and let it rotate fast so that eyes cannot track the movement of the blades, it looks like a blur. Now think of how eyes works. Simply the eyes register photons and by averaging over many photons an image is created and interpreted by the brain*. Noe look from below the fan towards ceiling. Since the fan blades are spinning fast the photons coming from the fan blades and also from the ceiling between fan blades. Since the blades are 50% of the area there is approximately 50% photons from fan blades and 50% photons from ceiling reaching the eyes of the observer. Result would be that brain interprets photons as coming from something like a half-transparent disc. For a fan with a color similar to ceiling and thinner blades the fan could look almost invisible or almost fully transparent. *) very simplified, hopefully correct enough for the context

No. It makes no difference; perpetual motion is not possible even if combining devices. The overall physical laws still applies.

I may have misinterpreted the following: Cosmic inflation does not seem to be as widely accepted as the expansion of the universe. Not all physicists* think there is enough evidence to support the phenomenon. The inflation phenomenon does not push away massive bodies. The inflation ended before massive bodies formed, inflation is an early period of accelerated expansion. Therefore I asked for a reference supporting your statements. Here is paper on cosmic inflation that might be a good introduction. https://arxiv.org/pdf/astro-ph/9901124.pdf. *) See for instance criticisms section on wikipedia: https://en.wikipedia.org/wiki/Inflation_(cosmology)#Criticisms

I think other members have responded in detail, I probably should have written that the photons in the EMP has zero invariant* mass. I find it interesting that there was an earlier concept of a specific "electromagnetic mass". Modern physics instead use mass–energy equivalence instead of electromagnetic mass, but it still can be found** in older material. Regarding steady vs constant***. For what it is worth Feynman says: "magnetic fields associated with steady currents—the subject of magnetostatics". I had to check since in my first language the meaning of steady, constant and related words sometimes kind of overlap with "reliable" current (free from unwanted fluctuations). *) or "rest" mass **) For instance "Electromagnetic mass", The Feynman Lectures on Physics, 2 http://www.feynmanlectures.caltech.edu/II_28.html

Thanks for the feedback! It's always good to know that an explanation was helpful so similar cases can be addressed in similar ways in the future. (Or that an explanation was not helpful and improvements are needed)

One part of the equation is moved to the right, note that the sign is changed (x-p) becomes (p-x) and the zero is not explicitly displayed. I highlighted that in image* below. The derivative dS/dx is set to 0, see the first zero i added. The expression for dS/dX is then expressed as function of x, p, q and restructured. On the second row I added the zero again to show the equality. *) Had to use phone, hard to create a good picture.

According to current theories inflation ended at some early time. You write as it is an ongoing phenomena: 1: Do you have a reference where atomic physicists state that inflation is pushing objects away? 2: Do you maybe mean the current expansion of the universe instead of the theory of early cosmic inflation?

I did not find a reference for the impact angle (yet) but found something else I did not know about. When scientists describe the hazard of a potential impact to the public they combine size, energy and probability into one figure. A really large object with very low probability of colliding with earth is given the same level as a smaller object that is calculated to be more likely to collide. https://cneos.jpl.nasa.gov/sentry/torino_scale.html https://en.wikipedia.org/wiki/Torino_scale

Thanks for the reminder! I had forgotten that! (I used that set of rules, quite a lot, a long time ago in analysis of AC circuits, made calculations easier wikipedia.org/Electrical_impedance )

An EMP consists of a mix of Electric field Magnetic field Electromagnetic radiation Electrical conduction None of these carry mass, but can carry momentum as far as I know.

(bold by me) I have (mis)interpreted the bold part to mean an identical number of heads and tails. So @Prometheus answer therefore may be more applicable.

Short note on the specific case in the question: when tossing 4 coins you calculated the probability of getting exactly 2 heads and 2 tails. When tossing same coins a finite number of times you did not ask for the probability that the outcome is exactly 1/2 heads and 1/2 tails. As you said it will be approaching 50% heads and 50% tails in the long run. The situations are different and requires different formulas. "Mathematics of probabilities" is a rather broad subject. Before attempting a longer explanation; are you questioning a more specific part of probabilities? For instance law of large numbers is applicable when discussing your question.

I usually copy/paste or drag and drop images into the edit box. Works fine from computer. Ok. Do you mean cosmic inflation? Cosmological inflation, or just inflation, is as far as I know a theory of exponential expansion of space in the early universe.