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Okay so back to tidal forces and size: Am I mistaken that being close to a super massive black hole you’d feel gentler tidal forces than close to a stellar mass sized black hole? What about if you were at the event horizon for each?

Ah yes, of course, you measure it, thus it is not coordinate dependent. So, as you cross the event horizon, blueshift at best would be moderate. Does this also depend on the size of the black hole? I am under the impression that tidal forces depend on the size (if altitude is the same, larger...

I am under the impression that an outside observer would see things redshifted as the person they are observing approaches the event horizon. So, it seems reasonable that someone from inside the black hole would see incoming light blueshifted. Is this inaccurate? Why or why not? If it is...

Perhaps, but look at the world we live in today. What was fringe fifteen years ago is now proudly shared online, and millions get their minds infected with things like flat Earth stupidity, QAnon stupidity, and on and on. We used to laugh at conspiracy theorists. Now they are making public...

There is one and only one type of source anyone should be trusting or posting here, IMHO: peer reviewed scientific publications.

This is excellent stuff. But since @mitochan brought up colliding BHs, I have a related follow up question: Nothing can travel faster than c, so would this not prevent two colliding BHs from ever instantly becoming one? Because presumably the two singularities are separated by a non-zero...

Let's say you have an absolutely giant black hole, so big that items inside of it leisurely approach the singularity, reaching it in about a million years (or whatever time it takes for a black hole to form from matter accumulation). Could matter slowly accumulating somehow form its own black...

Kind of makes you wonder why this isn’t being done already given it’s supposed to be intramuscular. Is it particularly time consuming? I wouldn’t know. EDIT — upon reading more, it seems the concern isn’t enough to make it a widely practiced part of IM injection.

I myself have wondered if that's even physically possible, with all the quantum weirdness. I'm of course fully ignorant about QM, but the thought has crossed my mind. Not that it matters, since in physics simplifying models are used to isolate particular paths of inquiry.

Excellent explanation. Thank you for coming back this. It is interesting, as PeterDonis pointed out in post #42, that you only have two choices. But seeing it this way helps me get a better a snapshot of all the balls that were being juggled by these people early in the 20th century trying to...

That’s a great Insight, but one thing I’ve wondered is why the concept of relativistic mass was even invented, other than the need to keep equations more familiar. Is there another more useful reason for it being created?

Not with knowledge of the term but I suppose yes. But yeah, as a student I will agree that standard Minkowski diagrams are more intuitive. Loedel diagrams may have some usefulness, but not at the expense of opening the door to more confusion. There’s enough unintuitive stuff to worry about...

Yes. But presumably you could use the simple Pythagorean trig identity by replacing ##γ^{-1}## with ##\frac{1}{γ}## could you not? (I wonder if that would be of use at all) That is, ##γ^{-2} = γ^{(^-1)(2)} = (\frac{1}{γ})^2## ##\beta^2+(\frac{1}{γ})^2 = 1## looks the same to me. But even if...

I was told by the nurse if you’re going to have a dangerous reaction, it’s most likely after. Maybe stay vigilant.

But that surely means you can easily change those to trig functions. I am now intrigued. That negative power raises a small problem, but surely there is a simple work around I’m missing. An i or something.

That is so sneaky. I like it.

There’s no way I can remember the study, but I read one that said that while peak viral load was the same for breakthrough cases as it was for unvaccinated, the viral load in vaccinated patients decreased much faster — which indicates they would spread it less over similar time windows.

My guess is that would have been 14-15 had everyone been unvaccinated.

That’s true. Quick general question to the biologists here: If R is reproduction number and E is vaccine effectiveness, does this formula tell the percentage we need to vaccinate to get herd immunity? ##\frac{1 - \frac{1}{R}}{E}## I can’t remember where I’ve seen that but it looks familiar.

All of those studies I clicked on said vaccination reduces chances of infection, some by a very large amount. I don’t understand the hold up here. Also one criticism I have of some studies on the topic is that some rely on patients reporting if they’re vaccinated or not, and I guarantee at...

Breakthrough infections are pretty rare compared to unvaccinated infections based on all the publications I have read.

Meanwhile a serious side effect of COVID 19 is death, and it’s way more common than these serious vaccine side effects.

You’re using the Galileo velocity addition formula, which is only accurate for speeds much less than c. https://en.m.wikipedia.org/wiki/Velocity-addition_formula

I actually have not at this point, which is weird, given that I have messed around with some of the (non-tensor) math. But that's not physics. I do plan on actually going through some of the problems in that Tipler book (I've actually bought it, so I won't be a total cheap-o and steal from the...

Yeah that’s just a writing error. I don’t know if you can see all my edits but I had a nightmare of LaTex issues, which screwed up my proof reading. I was supposed to be copying Tipler and just messed it up. What I’m curious about now, however, is why the choice of units gives a false...

Ah. Now that makes some sense. (from Hyperphysics via a google search) Which means it's just a unit coincidence that when written as I written it looks the opposite.

Just found another one by Tipler (Modern Physics, 4th ed.) that does something similar, but then it takes it into a direction that seems ripe for confusing me: since each momentum component has its own gamma, it expresses γ in terms of the primed coordinates, so you get γ. $$γ' = \frac{1}{...

Oh man I’m sorry. I’ll delete it. Also, in hindsight I can see how this approach is dangerously close to suggesting relativistic mass. Probably not a good approach. EDIT — that textbook does mention realistic mass shortly after that example, but then says for the duration of the book mass...

The purpose of all this is to trace the train of thought of someone new to the concept of momentum in relativity, someone who's been taught their whole life that p=mu and that this value is conserved, and how they might be convinced on an intuitive level. Someone who isn't well versed enough on...

Would you be kind enough to look at my last post? I have rephrased the question again and attempted a physical example to show what I'm hoping to show. Apologies. I completely messed up what I meant to say. What I mean is: (1) Start with ##dx##. (2) Divide by ##\frac{dt}{γ}##. That gives...

Thanks for your patience and effort, everyone. It is appreciated. I think I figured out a reasonable solution to my problem. But first, let me give the question a final phrasing that is as clear as I can get it: How do I show that classical momentum is not conserved in a universe where...

Thanks. That dawned upon me just a second ago.

Thanks. This is a little closer to my math level than the tensor stuff. I followed all of it, the expansion, and so on (I'm assuming the O means all members of the expansion of higher order) , but my only curiosity is the constant ##-mc^2##. I have the power of hindsight to know that that is...

That's true. But I feel like the answer to the gamma factor question will necessarily answer the other one. How about I look at it from a different approach: What if I wanted to derive the relativistic momentum equation, but NOT doing it the usual easy way (starting with a position...

Experimental data of course confirms that Newton's formula for momentum is inaccurate. But as far as I can tell, all you have to do to confirm SR is demonstrate that the speed of a beam of light is independent of the speed of its source. Honestly, it feels like to me that Einstein's simple...

I know. What I’m trying to do here is follow the reasoning that leads to the correct momentum representation.

I've seen an easy use of the Lagrangian to show that time translation invariance implies energy conservation. But how do you get that particular Lagrangian? (never mind the fact that I barely know what a tensor is, or how to decipher Einstein summation convention, of course ;) ) Following...

I think a more concise way to ask the question is this: If we use the Newtonian definition of momentum, it is not conserved in special relativity. Assuming the last sentence is true (I have heard it around in various physics discussions... I know, that's not an acceptable source. Apologies)...

Now, deriving relativistic momentum isn't terribly difficult, but that's not the same as understanding it. I'm trying to figure out why conservation of momentum in special relativity requires the gamma factor. When I looked at conservation of momentum in elementary physics, we basically just...

Oh one other thing: these discussions about what the meter is are not pedantic. As you learn more about this topic (speaking from personal experience), you’ll find that the rabbit hole goes much deeper than you might think. And with respect to the meter specifically, when Einstein was first...

Regarding being "shot down" here, be careful not to read too much intent into words. A lot of the time people here are extremely concise and to the point, and it can come across as being "shot down," when it's really just someone stating a fact with no embellishment or fanfare. What I mean is, a...

That’s true, but it feels to me like there’s a sense of symmetry when I think of it that way, like they are two subsets of a larger whole.

Well to be fair, while I appreciate the sentiment, where I was coming from was the general transformation derivation alluded to by PeroK, after making assumptions about isotropy and homogeneity space and time. With those assumptions, you’ll end up with only three possibilities: one which...

Looking at the algebra it seems to me like it boils down to whether the invariant speed limit is finite or infinite. If it’s finite, you get SR (and time dilation), and if it’s infinite you get Galileo (and no time dilation). I know I’ll probably get chastised for suggesting that an infinite...

(What follows disregards those with health issues that, according to the medical mainstream, makes them unsuitable for vaccines) Probably not. At the risk of getting banned, there doesn’t seem to be much that can be done to convince the under 100 IQ portion of the population, or those who...

I feel like the golden path can be found by comparing death rates, which overwhelmingly favor getting vaccinated.

I mean, honestly these are so uncommon I don’t see how simple coincidence isn’t as good an explanation.

Wish there was a way to separate correlation from causation here.

Here's another question I have for the biologists, since you mentioned this: would a virus or other infection that has been with humans for eons be easier to get rid of or control, since they have never experienced the pressure modern humans would put on them through vaccines and other measures...

Well, I was quoting out of context, but the general principle is obvious. Sidenote: if you've ever regularly attended a fundamentalist Assemblies of God church, as I did most of my life, using scripture out of context (and word origins as well) is a weekly thing. There is usually a theme...