Lorentz Jr

Except two axes would be across the grain.

I think the question was about something more substantial.

Okay, I take back the word "entire". I know the subject has been discussed by Peter Woit, Jim Baggott, Sabine Hossenfelder, Lee Smolin, and Roger Penrose. My understanding is that they're still in a fairly small minority though. I'm not sure what your point is, swanson. EDIT: Oh, you mean they don't write the word "just"? I'm pretty sure they have the same complaint in mind. "made up" meaning "fake", as opposed to what the author of the article describes.

The entire physics community has been evading the issue of "reality" (i.e. ontology) for over a century. Relativity and quantum mechanics suddenly made the question maddeningly difficult, so physicists copped out and gave up, saying "It's not our job. It's mere philosophy". Just like the fox and the grapes. The author (like most other professional physicists) misses the point of the question by ignoring the word "just". People don't complain that dark matter is something physicists made up, they complain that it's just something they made up, meaning it's not "real" in the sense that science is commonly expected to be (and was perceived to be in the 19th century). Many critics even explicitly make the analogy with epicycles as bad science that was motivated by religious narrow-mindedness. Of course, many of them are motivated by "physics envy", i.e. frustration that the geeks of the world have been getting so much attention and legitimacy for the last few centuries, and a common counter-argument by science advocates is that critics are projecting their own narrow-mindedness onto scientists. But the current mainstream counter-argument (which is repeated for the zillionth time in the article) is dangerous. It basically says it's okay to do bad science -- or at least shallow science -- until someone comes up with something better, and anyone who doesn't like it can go jump in a lake. But the bad science of string theory has been (or at least was recently) dominating theoretical physics research politically, suppressing more promising lines of research and wasting billions of dollars and the careers of thousands of bright theorists. Physicists risk a religious backlash if the community gets too corrupt and too dominated by unproductive pseudoscience.

Nonsense. Your answers have been unscientific fabrication: Which has nothing whatsoever to do with the comment you were responding to:

It's almost more like a dart than an airplane. Can't have a very good glide ratio being so stubby.

I knew that. It was obvious. It's also obvious that ranges can be finite. I'm not sure what either of your responses have to do with my comments.

because there is no "next" real number. The word "next" only has meaning in the context of countable sequences. Intuition won't help you understand the real number line, because your intuition (and everyone else's) is based on finite numbers and countable sequences.

That doesn't mean it's finite. The density of points is infinity divided by a finite number, which is also infinite. If the length of the closed interval is L, then you can think of the length of the open interval as the limit of L - dx as dx approaches zero. The difference is a finite number divided by infinity.

It's hard to comprehend because you're trying to apply the logic of finite numbers to infinities. What is an "end point"? You have a row of points, and it's the one at the end. But there may not be any "end" to the points when there's an infinite number of them.

[math]\displaystyle{ dt' = dt_s / \gamma } [/math] [math]\displaystyle{ t_{r1} = \frac{y + dy}{c} }[/math] [math]\displaystyle{ t_{r2} = \frac{ds}{v} + \frac{y}{c} }[/math] [math]\displaystyle{ dt_r = \frac{ds}{v} - \frac{dy}{c} }[/math] [math] dy = ds \sin \theta [/math] [math] dt' = dt_r [/math] [math] \displaystyle{ \frac{dt_s }{\gamma} = \frac{ds}{v} - \frac{dy}{c} }[/math] [math] \displaystyle{ \frac{ds }{\gamma v }= \frac{ds}{v} - \frac{ds \sin \theta}{c}} [/math] [math] c = \gamma c - \gamma v \sin\theta [/math] [math] \displaystyle{ \sin\theta = \frac{c}{v} \left( 1 - \frac{1}{\gamma}\right) } [/math]

Relativistic effects don't change the shape of the waveform. Whatever happens to the overall speed of the signal will also happen to the frequencies. The most "direct" way to listen in to the signal would be to have an array of listeners along the spaceship's path, each station receiving a short snippet as the spaceship passes. When you're in front of the spaceship, the signal will seem faster according to the Doppler formula, as Genady showed. When the line between you and the spaceship is perpendicular to the ship's velocity, the signal will seem time dilated by the usual gamma factor. So there must be some angle [math]\theta[/math] where the signal comes in at normal speed. If a time [math]dt_s [/math] passes in Earth's reference frame between two events on the spaceship, the interval in the spaceship will be [math]\displaystyle{ dt' = \frac{dt_s }{ \gamma} } [/math] If the ship travels a distance ds, from y = dy to y = 0 (so [math] dy = ds \sin \theta [/math]), during this time, and a receiver is a (relatively large) distance y (along the y axis) below the x axis, the time for the first light signal to reach the receiver will be [math]\displaystyle{ t_{r1} = \frac{y + dy}{c} }[/math] and the total time from when the first signal is sent to when the second signal is received will be [math]\displaystyle{ t_{r2} = \frac{ds}{v} + \frac{y}{c} }[/math] So the time interval for the receiver will be [math]\displaystyle{ dt_r = \frac{ds}{v} - \frac{dy}{c} }[/math] Now we set [math] dt' = dt_r [/math] to calculate [math]\theta[/math]: [math] \displaystyle{ \frac{dt_s }{\gamma} = \frac{ds}{v} - \frac{dy}{c} }[/math] [math] \displaystyle{ \frac{ds }{\gamma v }= \frac{ds}{v} - \frac{ds \sin \theta}{c}} [/math] [math] c = \gamma c - \gamma v \sin\theta [/math] [math] \displaystyle{ \sin\theta = \frac{c}{v} \left( 1 - \frac{1}{\gamma}\right) } [/math]

What do you mean by "listen in directly"?

You have provided incoherent nonsense. You're boring us, Mr. Bahari. Please post something funnier. 😄 Length contraction: [math]L' = {x'}_2 − {x'}_1 = \gamma(x_2 − vt)−\gamma(x_1 − vt)=\gamma(x_2 − x_1)=\gamma L[/math] Time dilation: [math]\displaystyle{\Delta t' = {t'}_2 − {t'}_1 = \gamma\left({t_2} −\frac{vx}{c^2}\right)−\gamma\left({t_1}−\frac{vx}{c^2}\right)=\gamma\left(x_2 − x_1\right)=\gamma\Delta t}[/math] No dependence on the sign of v. 😉

Bulk motion of nuclei is simple enough. That's just electromagnetic interactions between the protons and electrons and other nuclei. The hard part would be internal excitations of the nucleus. The short answer may be that they don't know for a while. Maybe a long while. The nuclear forces are short-range, so I wouldn't expect much from them.

Whatever. More and more workers are starting to realize that capitalism isn't helping them (r > g), many of them are turned off by cultural liberalism, and environmentalism doesn't really provide solutions to those problems.

Exactly. And they've been getting popular lately. Republicans and Evangelicals in the US, Orbán in Hungary, Duterte in the Philippines, Erdoğan in Turkey, Netanyahu's conservative coalition in Israel, AfD in Germany, Obrador in Mexico, Lukashenko in Belarus, and of course Putin, Xi, and Kim -- lots of countries turning to authoritarianism, religious and/or national.

Maybe liberal ideologies.

Young, university-educated Westerners.

Rupert Murodch's "greening" is just the rise of capitalism as the dominant belief system, and it's been happening all over the world for centuries, ever since corruption in the Catholic church led to the Enlightenment. It was obvious in the Roaring '20s, it accelerated in the 1950s (under the cover of Joe McCarthy's Red Scare), and it's been pretty much taken for granted since the 1980s, when the Berlin Wall fell and Ronald Reagan made "Liberal" a swear word. The FOX News thing is just one random event that will probably be eclipsed by bigger and even worse events in the not-too-distant future. What's really interesting is the resurgence of religious conservatism, which has also been rising globally and has the potential to unseat capitalism as the world's organizing philosophy. Environmentalism will always be around, but it doesn't inspire most people under most circumstances.

Yes, that seems to be the case. See the measurement problem. No one currently knows what happens in measurements, and the averaging out of quantum uncertainty in macroscopic objects has led to some bizarre interpretations of QM. My favorite candidate for bridging the gap is the Diósi–Penrose model, which says quantum states of macroscopic objects keep getting collapsed by their own gravity.

Your key point was that the transformations are asymmetric. That point is false.

v is defined as the speed of S' relative to S, given the convention that positive values are to the right (i.e. toward [math]+\infty[/math]) and negative values are to the left (toward [math]-\infty[/math]). There's nothing in the proof that requires v to be positive. Nonsense. There's no law against scalars being negative. EDIT: More accurately, v is a component of a vector, and vector components are allowed to be negative.

Too many trolls using things like that as excuses for abusing people, too many snowflakes taking everything literally these days.

That would be very massive! Also, I would like to see a link about the lensing. Usually the images are distorted.