How far could the sun possibly be?
profmattstrassler.com
profmattstrassler.com
But I have to follow up with: "Well, but... how do we really know?" A: We have followed up well worn paths of scientific inquiry, and looked at our assumptions, in designing an experiment that, we assume to fail. When it does not follow our assumption, then we can only rule out failure, and call it a success. This follows centuries of this type of exacting and painstaking scientific work. Although I would normally have 10 ~ 12 citations of very diverse work, that exercise is left to the reader.
But... how do you measure the diameter of the sun?
That Copernicus got there at all is incredible
We already know the distance. About 8 light minutes away.
The question of the parent comment was "how do you measure the diameter of the sun?"
Apparently the only pre-modern people (i.e. pre-Giordano Bruno) recorded as making the claim were Anaxagoras and Aristarchus of Samos, but their ideas were completely rejected by contemporaries:
https://solar-center.stanford.edu/FAQ/Qsunasstar.html
In retrospect, it just seems so blindingly obvious that I'm tempted to believe that I too would have seen through the Aristotelean BS.
But surely there must be aspects of reality that will seem similarly obvious to future generations, and yet I don't feel any insights coming on.
I should say, Aristarchus is the ideal of maximizing information from minimal data:
"Aristarchus of Samos (Samos is a Greek island in the Aegean Sea) lived from about 310 to 230 BC, about 2250 years ago. He measured the size and distance of the Sun and, though his observations were inaccurate, found that the Sun is much larger than the Earth. Aristarchus then suggested that the small Earth orbits around the big Sun rather than the other way around, and he also suspected that stars were nothing but distant suns, but his ideas were rejected and later forgotten, and he, too, was threatened for suggesting such things."
Evidence in favour: The sun is a light source, they are much dimmer light sources with much smaller radii, consistent with the hypothesis.
Evidence against: There are none at intermediate distance, they're either the sun or so far away to practically be a point light [1]. The sun is yellow, they are not [2]. The sun has a partner in size (measured in portion of the sky it takes up) with the moon, which I presumably know is relatively close by, suggesting some form of relation between them [3].
Ultimately I know that there are lots of ways to give off light. Fire, fireflys, lightning, the sun (if it isn't fire), hot metal, sparks from static electricity, ... There just isn't enough evidence to believe that it's more likely that the stars are the same source as the sun than yet another source.
[1] As it turns out "so far away to be a point light" is the intermediate distance, but that result requires an amount of empty space that I would find unlikely. I haven't checked this but I suspect a statistical analysis would also find it unlikely. Assuming all stars are the same size as our sun, and that they're distributed uniformly in space. Given that I count the stars and come up with a reasonable minimum and maximum distance bound from their brightness, I suspect it is extremely unlikely that there are as many as there are but none close enough to be noticeably brighter. This result (assuming it is true) is of course the result of the fact that many stars are far larger/brighter than the sun, so we're actually sampling from a much larger volume than my naive estimate suggests.
[2] I'm not sure I fully understand this one... the sun appears yellow because of some quirk to do with the light the atmosphere lets in, but why doesn't that make the other stars yellow too?
[3] Pure coincidence
Most stars appear white/bluish because they are too dim for our colour receptors to perceive. The spectra arriving at our eyeballs is consistent with what you would expect given the type of star, redshift, and atmospheric conditions, but the perceived colour is not.
Hm, I don't expect many people feel this way!
So people promoting distant stars had a glaring contradiction they had to ignore. Lesson for modern theorizing.
https://terrytao.files.wordpress.com/2017/11/cosmic-distance...
https://www.youtube.com/playlist?list=PLldN_DpkXL3ZQWmwmwIze...
Now do GR.
Which is totally obvious, so I suspect that means that I missed your point. Could you clarify?
For experiment 1, say I accelerate the clocks at 0.1 g for 10 seconds, then drive with constant velocity for 1 hour, then decelerate at 0.1 g for 10 seconds. That acceleration time dilation exactly matches the change in propagation time due to the difference in c? Fine, I'll give you that.
So for experiment 2, I drive at constant velocity for two hours. I've kept the acceleration time dilation the same as in experiment 1, but doubled the distance. If the change in propagation time matched in experiment 1, it can't match now.
Or, for experiment 3, I accelerate at 0.1 g for five seconds, reaching 1/4 of the previous velocity, then drive for two hours. Now the propagation difference is the same as in experiment 1, but the acceleration time dilation is different.
So how is this going to come out "you can't tell" in all three experiments?
1 hour according to who's clock? The point is that if the 1 way speed of light is different, the clocks traveling in opposite directs will measure the 1 hour passing at different speeds.
But what if I don't know what c is? Doesn't matter. I know it's much, much larger than the velocity I'm moving at.
So I don't buy the "according to who's clock" argument. I can make it so that it doesn't matter, just by going slow enough.
If all the clocks agree at the satellite facilities, then I have established that space is isotropic for the slow transport of clocks (or at least, it is isotropic for the paths chosen - a skeptic can always device a "sufficiently smart anisotropy" that would appear to be isotropic for the paths chosen). Per the article, that was one of the assumptions that couldn't be trusted, but if we can experimentally establish it, we can trust it.
We now have synchronized clocks at the two satellite facilities. (We know they're synchronized because we established that space is anisotropic to the slow transport of clocks, and also because at least some of the clocks were transported with identical profiles in opposite directions.) We can now use time of receipt minus time of transmit to establish the one-way speed of light.
Doesn’t matter how careful you are, SR tells us moving clock will become unsynched. The amount of “unsynching” depends on c (see Lorentz factor) so if c is different in forward vs reverse direction, bringing the clocks back will even it out
No you wouldn’t be able to “see” it. If your clocks are off you dont know that and by how much until you bring it back and compare. That's Special Relativity
The idea is that you can't know this. You're somewhere in the middle receiving messages from all the clocks, and you can't tell if they're synchronized unless you've already defined the speed of light between you and each clock.
Second, I was thinking of labs perhaps tens of km apart. You can have people at the center, and at satellite facility A, and at satellite facility B.
Put another way: the speed of any signal or causality coming back from your measuring device is always a factor with no way around that.
I dealt with that by moving the clocks with identical velocity profiles, so time dilation should be the same...
Unless time dilation is anisotropic. I dealt with that by sending multiple clocks, with some sent on triangular routes and some direct. In more detail:
C
A B
D
But the point is, if I can show that time dilation is anisotropic, then the clocks that went direct from A to B, and the clocks that went the same distance in exactly the opposite direction, should have the same time on them.
You mean isotropic, and you don't really. D->B is the same as A->C and C->B is the same as A->D; whatever clever path you come up with, a clock going from A to B will end up having had vertical movements that sum up to 0. If moving up induces some extra time dilation and moving down reduces it, or vice versa, you'll never be able to detect it; ultimately you can only ever make measurements when you and your clocks (and/or signals) have moved in closed loops, however squiggly.
But I see what you mean about the sides (as drawn) being parallel.
And, yes, I meant isotropic, not anisotropic. Embarrassing.
OK, how about this: I have an equilateral triangle, with vertices A, B, and C. I synchronize clocks four clocks at A. I send one clock to B directly, and one to C and then B. I send one clock to C directly, and one to B and then C. I do the same from points B and C. Then, I can look at the difference between clocks that came direct and clocks that came the long way. If all the differences are the same, then I can say that going A-to-B-to-C has the same effect as going A-to-C-to-B or B-to-A-to-C or any other route. Doesn't that show isotropy?
Again, no, because you can only measure around the full loop. Any clock you can compare has gone just as far east as it has gone west, just as far north as south, and just as far up as down. You can rule out some particular kinds of anisotropy, but there are possible patterns that just wouldn't show up.
https://en.wikipedia.org/wiki/Redshift:
“The main causes of electromagnetic redshift in astronomy and cosmology are the relative motions of radiation sources, which give rise to the relativistic Doppler effect, and gravitational potentials, which gravitationally redshift escaping radiation. All sufficiently distant light sources show cosmological redshift corresponding to recession speeds proportional to their distances from Earth, a fact known as Hubble's law that implies the universe is expanding.”
"gravitational redshift (known as Einstein shift in older literature)[1][2] is the phenomenon that electromagnetic waves or photons travelling out of a gravitational well (seem to) lose energy. This loss of energy corresponds to a decrease in the wave frequency and increase in the wavelength, known more generally as a redshift. "
It is possible that physics conspires such that the speed of light is direction dependent, but that it averages out if half your path is the exact opposite direction from the other. I think this can be excluded by comparing more complicated paths; although the nessesity for it to form a closed loop might be give physics an unavoidable out if it really wanted to mess with us.
There are also theories where the speed of light differs based on direction; but space itself differs in the same way, canceling the effect. These are fundamentally equivelent to a theory where both are constant.
Later, Richard Feynman used first principals to both confirm this for Enistienien physics, and break it for quantum physics.
The best reference for this work is not the classic experiment, but on Henry Cavindish's balance, which led to the calculation of G, the gravitation constant to 7 digits of accuracy, based upon the speed of light calculated to 9+ digits of accuracy.
The speed of light is invariant: What you the observer actually see, is a frame of reference in space-time, which transforms the space, so that light still travels as fast as it always does, but the space around it is transformed.
There have been a few theories of exceptional note: Sir Fred Hoyle solved Einsteins equations for an invariant size of the universe based on a shrinking frame of reference, and found no contradictions. Hence the wimper theory of cosmogony. I count myself as pretty bright, on this subject, able to argue the point rather succinctly, but I never claim to hold a candle and a mirror ( Cavendish ) to Henry Cavendish, nor Sir Fredric Hoyle: You want to get the real brilliance of this total failure:
"The Michelson-Morley Experiment (MMX) tried to prove the existence of ether, but they did not observe the movement of interference fringes, which led to the assumption that the speed of light is constant in the inertial reference frame, which is also the theoretical basis of Einstein's special relativity (SR)."
It failed to prove the existence of ether. Failed. Richard Feynman also found that for Eisensteinian physics, this was also true from first principals. This is really one of the most brilliant failures in the history of Physics.
“Success is the ability to go from failure to failure without losing your enthusiasm” ― Winston Churchill
The fixed exchange rate between pounds and kg is obsolete and inappropriate for a modern economy and is the kind of thing BREXIT was supposed to free us from.
It's wonderful that we have different miles and feet for different purposes, and even different exchange rates between them.
Let the Europeans suffer under the yoke of the rigid and procrustean french measurement system. Let freedom of expression flourish!
"Since the revision of the SI on 20 May 2019, we can now compare the gravitational force on an object with an electromagnetic force using a Kibble balance. This allows the kilogram to be defined in term of a fixed numerical value of the Planck constant, a constant which will not change over time."
"A Kibble balance is an electromechanical measuring instrument that measures the weight of a test object very precisely by the electric current and voltage needed to produce a compensating force. It is a metrological instrument that can realize the definition of the kilogram unit of mass based on fundamental constants."
"One important reason for the change is that Big K is not constant. It has lost around 50 micrograms (about the mass of an eyelash) since it was created. But, frustratingly, when Big K loses mass, it's still exactly one kilogram, per the current definition. When Big K changes, everything else has to adjust."
Not sure if this is a joke about weights changing over time or in different places due to gravitational differences - but if you mean mass that was true until fairly recently, the kg is no longer defined by the mass of a specific physical item.
"Since 1 July 1959, the international avoirdupois pound (symbol lb) has been defined as exactly 0.45359237 kg. In the United Kingdom, the use of the international pound was implemented in the Weights and Measures Act 1963. (a) the yard shall be 0.9144 metre exactly; (b) the pound shall be 0.45359237 kilogram exactly."
"The kilogram is defined by taking the fixed numerical value of the Planck constant, ℎ, to be 6.626 070 15 × 10-34 when expressed in the unit J s, which is equal to kg m2 s−1, where the metre and the second are defined in terms of the speed of light, , and the hyperfine transition frequency of the caesium-133 atom..."
Nothing new. Rando hacker news poster, vs say... the International Standards Organization on Weights and measures. Hmm... I am going to place my faith in say... a group of people who's degrees far outnumber most of the colleges I studied at.
No, the speed of light is not defied in the "flattest" one of them. Please do your homework. "The speed of light is a universal constant denoted by c."
In my second college physics class, the final exam was one single question: "Derive the speed of light." I got a grade of 4/10, which put me at the top two students in the class. The class was a 5 1/2 month exercise in brutality of math. I would suggest you get a few college physics classes under your belt.
Incorrect. It is two-way you’re measuring. Always. Yes, including in circuit designs
Nope it can't. See https://www.youtube.com/watch?v=pTn6Ewhb27k&t=0s for a good explanation.
You can possibly imagine a world where some of this asymmetry is from a lorentzian ether.
The below paper goes into complete technical details giving an example of the speed of light being c / 2 in one direction and instantaneous in another direction (so that it averages out to c), and how the differing time dilations result an isotropic view of the universe.
-- Douglas Adams
But the cosmic microwave background defines an absolute rest frame that we happen to be measured going 600km/s against. And you can measure one-way speed relative to that, provided you admit that, yes, you really can synchronize displaced clocks entirely adequately for the purpose, as we do absolutely routinely for GPS satellites in wacky orbits thousands of miles apart. Your measurement had better have the time-to-traverse from you to a clock indicating an extra 600km/s in that direction, and short the same in the other direction, and equal toward clocks placed at right angles to those directions. If it doesn't turn out to match CMB asymmetry, you probably get a Nobel prize.
On the subject of the CMB, some of the measurements show a bias exactly aligned with the plane of the solar ecliptic. This is called the "Axis of Evil" in astronomy circles, and is rarely mentioned as it is deeply embarrassing to cosmologists. "Cosmologists are often in error, but never in doubt." -- Lev Landau.
You could repeat the experiment at different times of the Plutonian year to verify other directions, etc..
I think there may be practical problems with this method in terms of creating such a well columnated laser pulse, but in principle couldn't we use it to rule out anisotropic light speeds in several (perhaps most/all) directions?
You could probably figure out the distance by using a technique we use to figure out the distance to nearby stars, measuring the change in position in the sky relative to very far away stars. I think you'd only need to observe two stars to figure out the distance.
Could also use pulsar timing like gps signals to track the location of the Earth throughout its orbit.
Could also take measurements after launching a pair of space probes away from the earth.
The distance of Venus was measured by the parallax method during a transit, with a baseline on the Earth's surface. This then yields all the other planets' distances from their orbital periods. This has me wondering why this had not been done for the Sun's distance, and perhaps the first reason to be considered is the difficulty of observing the Sun eclipsing distant stars.
Update: According to Wikipedia [1], Jeremiah Horrocks came up with reasonable figures for both the size of Venus and the distance of the Earth from the Sun from a single observation of a transit, but the article says he made use of a false premise, so does that just mean he was lucky?
[1] https://en.wikipedia.org/wiki/Transit_of_Venus#1639_%E2%80%9...