The Flat Earth Society
Flat Earth Discussion Boards => Flat Earth Theory => Topic started by: Jeb Kermin on August 03, 2020, 09:40:42 PM
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In the Wiki it is stated
https://wiki.tfes.org/Eratosthenes_on_Diameter
We can use Eratosthenes' shadow experiment to determine the diameter of the flat earth.
Syene and Alexandria are two North-South points with a distance of 500 miles. Eratosthenes discovered through the shadow experiment that while the sun was exactly overhead of one city, it was 7°12' south of zenith at the other city.
7°12' makes a sweep of 1/25th of the FE's total longitude from 90°N to 90°S (radius).
Therefore we can take the distance of 500 miles, multiply by 25, and find that the radius of the flat earth is about 12,250 miles. Doubling that figure for the diameter we get a figure of 25,000 miles.
However, I am confused about how this claim can be made. Here is an simple diagram of the situation (no tto scale)
(https://i.imgur.com/I4GPKZO.png)
It is claimed, that on a flat earth, that if we know D, the distance between Syene and Alexandria, we know the angle of A, that we can compute De (diameter of the earth in a 'flat disc' model)
However, I do not see how this can be done. Without going into the geometry. Imagine extending De to any aribtrary length. It will not change the angle A, nor the distance D. Therefore, for any given A or D, maps to any De > D at least (which would be obvious)
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If the sun moves across the sky consistently or near-consistently (by observation), and if the 500 mile distance between those two points is 1/25th of the total longitude radius of the Monopole model (90°S - 90°N), then the Monopole model can be computed to have a radius of 12,250 miles. Double for the diameter to get 25,000 miles.
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If the sun moves across the sky consistently or near-consistently (by observation), and if the 500 mile distance between those two points is 1/25th of the total longitude radius of the Monopole model (90°S - 90°N), then the Monopole model can be computed to have a radius of 12,250 miles. Double for the diameter to get 25,000 miles.
I'm still not quite following you - could you provide a diagram for what you mean? I also don't see anything in the wiki about the consistency of the motion of the sun coming into play here.
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(https://i.imgur.com/lDkIy8a.png)
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First off, this measurement was not made at the north pole, but much further south (in Egypt. Also degrees, as a unit of measure of an angles, have no definition along a straight line. They only have a definition as fraction of the circumference of a circular. (The full circumference represents an angle of 360 degrees, half circle 180 degrees, etc.). They are also defined by the intersection of two lines, because you can construct a circular arc of radius 1 originating at the intersection point which begins at one line at ends at the other. You can do this physically with a protractor. So I'm not sure how you can justify labelling the north pole as 90 degrees (or any other degree measurement, really), assuming a flat earth model.
I also do not see the intersection of any lines, or anything that represents an angle, which correspond to the red line that is supposed to represent 1/25 of the radius, so I'm not how the measurement of 7°12' is coming into play here.
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If the sun moves across the sky consistently or near-consistently (by observation)
...then that proves the sun can't be going in a circle above us. Otherwise the angular size and speed would constantly change.
and if the 500 mile distance between those two points is 1/25th of the total longitude radius of the Monopole model
And how do you establish that?
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If the sun moves across the sky consistently or near-consistently (by observation), and if the 500 mile distance between those two points is 1/25th of the total longitude radius of the Monopole model (90°S - 90°N), then the Monopole model can be computed to have a radius of 12,250 miles. Double for the diameter to get 25,000 miles.
All you're doing is multiplying by 25 because you have defined/presumed/assumed the 500 miles to be 1/25th. You have not shown how you have established that it is so.
Angles are defined as the displacement between two straight line vectors, at the point where the vectors meet. Writing 90 degrees N on your diagram does not show these vectors. Where are they, and where is the angle drawn?
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First off, this measurement was not made at the north pole, but much further south (in Egypt. Also degrees, as a unit of measure of an angles, have no definition along a straight line. They only have a definition as fraction of the circumference of a circular. (The full circumference represents an angle of 360 degrees, half circle 180 degrees, etc.). They are also defined by the intersection of two lines, because you can construct a circular arc of radius 1 originating at the intersection point which begins at one line at ends at the other. You can do this physically with a protractor. So I'm not sure how you can justify labelling the north pole as 90 degrees (or any other degree measurement, really), assuming a flat earth model.
I also do not see the intersection of any lines, or anything that represents an angle, which correspond to the red line that is supposed to represent 1/25 of the radius, so I'm not how the measurement of 7°12' is coming into play here.
7°12' is 1/25th of 180 degrees.
If you move North to South from one side to the Sun's area of light to the other side the Sun will rise from the horizon and make a 180 degree arc over your head.
Therefore we can take the known distance and multiply by 25 to get that distance across the sunlight area. If we think that the Sun is moving in a circle like the Monopole model we can double our figure for the total diameter.
It's really just measuring the N-S sunlight diameter on one side and then multiplying by two to get total diameter dimensions for a model.
I determined that the sun goes around the Monopole model because I read the FAQ.
I determined that the sun would rise and eventually set when you move towards it from one side of its area of light to the other based the sun's rising and setting over the course of a day.
I determined that the Sun would move consistently or near-consistently in the sky by observation.
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First off, this measurement was not made at the north pole, but much further south (in Egypt. Also degrees, as a unit of measure of an angles, have no definition along a straight line. They only have a definition as fraction of the circumference of a circular. (The full circumference represents an angle of 360 degrees, half circle 180 degrees, etc.). They are also defined by the intersection of two lines, because you can construct a circular arc of radius 1 originating at the intersection point which begins at one line at ends at the other. You can do this physically with a protractor. So I'm not sure how you can justify labelling the north pole as 90 degrees (or any other degree measurement, really), assuming a flat earth model.
I also do not see the intersection of any lines, or anything that represents an angle, which correspond to the red line that is supposed to represent 1/25 of the radius, so I'm not how the measurement of 7°12' is coming into play here.
7°12' is 1/25th of 180 degrees.
If you move North to South from one side to the Sun's area of light to the other side the Sun will rise from the horizon and make 180 degrees arc over your head.
When you say "move North to South", I presume you mean from a given point towards the closest point on the outer edge of the disc (which would be away from the North Pole).
Herein lies the problem. It will be impossible for an observer on a flat disc to ever observe the Sun at/below the horizon, at the same time another observer at another point of the disc observes it directly overhead, (or really, any point substantially above the horizon). Let me illustrate. Keep in mind this is a side view.
(https://i.imgur.com/NT8YCWA.png)
Observer O observe the sun directly overhead (90 degrees). Observer A will observe at some angle < 90 degrees. Observer B will observe the sun at a some angle < 90 degrees. As we imagine observer B getting farther and farther away from A and O, the angle keeps diminishing, this is true. But you cannot imagine even getting close to the horizon (an angle of 0 degrees), until observer B is very far away.
But we can better than just intuitive observations - we can actually do the math to determine how far B must be from A or O, in order to observe the sun at some given angle.
I'll use the following convention. ang(X) is the angle formed at point X, between the line from X to the sun, and line of the ground. In terms of Erathosnes, it would be 90 - the angle of the shadow formed in his stick experiment. For example, ang(O) = 90 degrees. dist(X, Y) is the distance from point X to Y. Also, though I didn't label it, I'll use S for the sun.
This following requires trigonmetry. Since we have a right triangle (one where one of the angles is 90 degrees), we can easily solve for lengths if we know one of them and angle between one of the sides.
In a right triangle, there will two line segments which are short, and a third line segment which is longer than the other two. This is called the hypotenuse.
There is a cool function, called "sine", which is defined for a given angle, assuming the hypotenuse is 1. It is writen as sin(X), reading as "the sine of X" sin(X) would be the length of the side opposite that angle. Since the hypotenuse is 1, sine can never assume a value > 1. In a real right triangle, where the hypotenuse > 1, we can simply multiply sin(X) by the hypotenuse to get the length of the opposite side.
There is also a similar function called "cosine", similar to sin. This gives you the length of the adjacent side to the angle. It is written as cos(X). cos(X) * length of hypotenuse gives the length of the side
Also I shoudl note, when using angles in the sine and cosine functions, you need to plug them in as "radians". Radians are defined as the length of the circular arc formed by the angle assuming a radius of 1. The circumfrence of a half circle is defined to be PI, which is roughly 3.141527. This correspondes to 180 degrees. So the conversion from degrees to radians is radians = PI * degrees / 180.
Looking at the diagram again, we can see both triangles share a common side, which is dist(O, S). We can use trigonometry to solve for the dist(B, O), if we have enough information.
In this case, we know ang(A), we know ang(O), we know dist(A, O), and we are presuming ang(B) The issue is to determine the dist(B, O) which satisfies the observations.
Now lets write down some equations, just going by the trigonometry
1) dist(B, S)*sin(B) = dist(O, S)
2) dist(B, S)*cos(B) = dist(B, O)
3) dist(A, S)*sin(A) = dist(O, S)
4) dist(A, S)*cos(A) = dist(A, O)
Equation (2) is the one we want to solve for, dist(B, O). However, we do not know dist(B, S). But we can use equation (1) to solve for dist(B,S). Dividing both sides by sin(B), we get
5) dist(B,S) = dist(O,S)/sin(B).
Now the problem is we don't know dist(O,S). But we can use equations 3) and 4) to solve for it. Equation 3) gives us the exac trelation - the only problem is that we don't know dist(A,S). But we can use equation 4, dividing both sides by cos(A), we get
6) dist(A, S) = dist(A,O)/cos(A)
Plugging this back into (3), we get
3) dist(A, S) * sin(A) = dist(O, S)
7) (dist(A,O)/cos(A)) * sin(A) = dist(O, S)
Now plugging this back into equation (5)
5) dist(B,S) = dist(O,S)/sin(B).
9) dist(B,S) = [ dist(A,O)/cos(A)) * sin(A) ] /sin(B).
Now we plug this back into (2) to solve for dist(B, O)
2) dist(B, S)*cos(B) = dist(B, O)
10) [[ dist(A,O)/cos(A)) * sin(A) ] /sin(B) ] * cos(B) = dist(B.O)
And we ended up with a mess, however a mess that can be calculated.
Now let's plug in Erathosnes numbers, and a reasonable number for ang(B), like lets say 5 degrees. He observe an angle of 7.2 degrees, which means that ang(A) = 90 - 7.2 = 82.8 degrees angle of the sun above the horizon. The distance, dist(A, O) was 500 miles.
So dist(B,O) = [[ (dist(A,O)/cos(A)) * sin(A) ] /sin(B) ] * cos(B)
= [[ (500 / cos(A * PI/180)) * sin(A * PI/ 180) ] / sin (B * PI / 180) ] * cos ( B*PI/180)
= 45239.09 miles.
The claimed diameter of the Earth in the wiki was 25,000 miles. And we weren't actually measuring the diameter, but something less than the radius. What that means the diameter woud have to be more than twice our number, so > 90,000 miles.
And this is assuming an angle of 5 degrees, as a I felt that was reasonable. But lets see what happens to our numbers as they get closer to 0 degrees.
For 2 degrees, we have dist(B, O) = 113339 miles ( to the nearest mile)
For 1 degrees, we have dist(B, O) = 226748 miles (to the nearest mile )
For 0.1 degrees we have dist(B, O = 2267711 miles (to the nearest mile)
So we can see whats going on, as we get closer and closer to 0, the distance is increasing very quickly. In fact looking back out our equation, since we are dividing by sin(B), it cannot be zero otherwise the value is undefined. sin(B) is only zero when B itself is 0, i.e, the sun is at the horizon. The model predicts that we can never get far enough away, to actually observe this.
Now, I suppose you could introduce that the idea that the light from the sun is doing something funny which causes it not to move in a straight line (refracting, accelerating, etc.) causing the observation you get. But, when do that, it trashes the basic geometry of the problem, such that he observations themselves worthless without knowing what the light is doing/ why it is doing that.
Therefore we can take the known distance and multiply by 25 to get that distance across the sunlight area. If we think that the Sun is moving in a circle like the Monopole model we can double our figure for the total diameter.
It's really just measuring the sunlight area on one side and then multiplying by two to get dimensions for a model.
I determined that the sun goes around the Monopole model because I read the FAQ.
I determined that the sun would rise and eventually set when you move towards it from one side of its area of light to the other based the sun's rising and setting over the course of a day.
I determined that the Sun would move consistently or near-consistently in the sky by observation.
The sun moving consistently in the sky at a given point, over the course of the year, is another problem (it doesn't, it varies over the course of a year at any given point), but I'll put that issue aside for now. Right now I want to focus on the basic geometrical reasoning.
So, in conclusion, it is my position that, assuming a flat Earth, Eratosthenes experiment can tell you nothing about the diameter of the Earth.
As a addendum, I'll note that I am not trying to necessarily argue for an alternate mode such as RET. I am simply working out the claims of FET, as claimed in that section of the Wiki, to its rational conclusions given basic geometrical reasoning.
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Herein lies the problem. It will be impossible for an observer on a flat disc to ever observe the Sun at/below the horizon, at the same time another observer at another point of the disc observes it directly overhead, (or really, any point substantially above the horizon). Let me illustrate.
This is an entirely different argument related to the nature of light and perspective and how they operate at large scales, which you are proposing to be indisputably true.
We observe that the sun sets, therefore there must be a mechanism which makes this happen. We also observe the sun move consistently, or near consistently, and so therefore there must be a mechanism that makes this happen. Observationally, there must be mechanisms which make those things happen.
All of this is rather unconnected to this discussion of using the sunlight area to determine the diameter of the Monopole model. You are asking an entirely different question of "why" the sun sets, which is unconnected to the empirical observation of seeing the sun set. For this follow up question you should see what we have to say about it.
See: https://wiki.tfes.org/Sunrise_and_Sunset
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Herein lies the problem. It will be impossible for an observer on a flat disc to ever observe the Sun at/below the horizon, at the same time another observer at another point of the disc observes it directly overhead, (or really, any point substantially above the horizon). Let me illustrate.
This is an entirely different argument related to the nature of light and perspective and how they operate at large scales, which you are proposing to be indisputably true.
We observe that the sun sets, therefore there must be a mechanism which makes this happen.
See: https://wiki.tfes.org/Sunrise_and_Sunset
All of this is rather unconnected to this discussion of the model, unless you want to prove your assumed axioms.
My assume axioms are basic Euclidean space (the 3d dimensional extension of 2d Euclidean plane geometry), and that light, at least this particular circumstance of the Sun to Earth observer, is (mostly) following a straight line path.
If FET is going to advance alternative axioms, such as non-Euclidean geometries, or that the light from the Sun to Earth does not travel in a straight line path in the circumstances we have here, this needs to be stated. It also should be quantified, when making quantifiable predictions such as measuring the diameter of the Earth based on measurements like Erathosnes. Otherwise it is impossible to work out the logical conclusions of the theory.
So I would ask the following questoins
1) Is Euclidean space an accurate representation of reality, at least in most circumstances?
2) If the answer to (1) is no, what geometry model is FET using? (hyperbolic and elliptic are two alternative geometries)
3) If the answer to question (1) is yes, does light follow straight line path, at least in some circumstances, such that your re able to determine the actual position of objects (X,Y,Z) coordinates in three dimensional space given multiple simultaneous observations from observers located some distance part? Or alternatively, multiple observations over time from different perspectives assuming the object is stationary?
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I am still waiting for a picture of the flat earth. Of all the people in boats , planes , balloons ,,,,,,nobody has a camera...., Why do sailing vessels show the top of their masts first when arriving to port and last when leaving port
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We observe that the sun sets, therefore there must be a mechanism which makes this happen. We also observe the sun move consistently, or near consistently, and so therefore there must be a mechanism that makes this happen. Observationally, there must be mechanisms which make those things happen.
You're an Occam's Razor kinda guy. If something maintains a consistent angular size then what's the simplest explanation?
If something is occluded by another object then what's the simplest explanation?
You only have to invent mechanisms if you discount the simplest explanations...
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We observe that the sun sets, therefore there must be a mechanism which makes this happen.
We do indeed. Seeing the Sun setting in the west and rising in the east must be among the most observed sky phenomenon out there. I think most people the world over understand why the Sun rises and sets. As did the ancient Greeks (and probably civilisations before them). However it seems that understanding hasn't manifested itself on Tom Bishop yet. He prefers to call it a 'mechanism'.
I guess this is the result of refusing to accept that the Earth is anything else but flat. In other words it is a self-created problem.
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What reason is there to believe that particles or waves travel in perfect straight lines through the universe without being affected by any phenomena? Can you answer more with than "they just do" and "Newton said..."? That doesn't sound so logical to me. Straight line trajectories are rather rare in human experience. The fact is that you are insisting on your assumption. All of your mechanisms have sets of axioms assumed.
When the edge of the sun is touching the horizon RE also says that it is already below it due to astronomical refraction. It is proposing that we see a consistent illusion every day.
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Why do you find it necessary to question something which is so blatantly obvious to 99.9% of the population? Do you just like to argue about things for the sake of it? Or it is just a case of you like to think you are right and everyone else is wrong?
Honestly Tom there are bigger problems to solve in the world than why the Sun rises and sets. We solved that one a LONG time ago. It doesn't take a genius to work it out.
The fact is that you are insisting on your assumption
No I am not. I am simply watching something happen in the sky (on a daily basis) and coming to a logical conclusion as to why it happens. Why don't you try it sometime rather than trying to re-invent how science explains the simplest of observations.
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What reason is there to believe that particles or waves travel in perfect straight lines through the universe without being affected by any phenomena? Can you answer more with than "they just do" and "Newton said..."? That doesn't sound so logical to me. Straight line trajectories are rather rare in human experience. The fact is that you are insisting on your assumption. All of your mechanisms have sets of axioms assumed.
We assume light travels in a straight line unless otherwise deflected because that is what we observe. We know light refracts when entering different densities, we know it bends when passing through massive gravitational wells, and we understand the mechanics and behaviors of these. Unless affected by a known mechanic, light travels in straight lines.
One piece of evidence is the Voyager probes, the New Horizon probes and the Mars robots. All of these are sent on gravitational assisted trajectories based on Newton mechanics, we point our telescopes and radio antennas where we predict their positions should be and can communicate with them. If light didn't travel in straight lines then we would not be able to talk with them. The two systems match up, the orbital mechanics say they should be at a specific spot, and that's where we find them.
Another point in favor is again the robots on Mars and other solar system probes are looking at the solar system from many different angles, some on the other side of the sun, and they all see what we would expect. If light were bending or curving in unexpected ways then those probes would see the planets in different positions than expected. Remember the pale blue dot picture, Voyager turned around to take a photo of the Earth, and it was right were it should be. This wouldn't be the case if light were bending in unknown ways.
A large amount of cross-checked observational data and many different physics systems all give consistent results. Science doesn't just assume things go straight, it has come to that conclusion due to the evidence and observations we have made.
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What reason is there to believe that particles or waves travel in perfect straight lines through the universe without being affected by any phenomena?
It's the most straightforward explanation. Occam's Razor.
There is absolutely no reason to presume that the light deviates in any fashion around a straight line connecting observer and object unless something can be positively indicated which will affect the light.
If you wish to assert it does not follow a straight line, you must first positively identify the phenomenon/phenomena to which you refer. In the absence of any, Occam's Razor prevails.
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Imagining a phenomena that travels in a straight line trajectory isn't "simple". It literally contradicts most known trajectories of particles and objects. You made a statement that straight line trajectories exist in nature and are the simplest idea when you have a difficult time showing examples of such that occur in human experience.
Even dropping a body under 'gravity' doesn't go straight in the presence of air resistance. Straight trajectories are artificial and unnatural.
We know from the double slit experiment that light propagates as a wave anyway, bending and propagating in complex ways and not in straight line trajectories. Straight isn't the default there.
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Imagining a phenomena that travels in a straight line trajectory isn't "simple". It literally contradicts most known trajectories of particles and objects. You made a statement that straight line trajectories exist in nature and are the simplest idea when you have a difficult time showing examples of such that occur in human experience.
Even dropping a body under 'gravity' doesn't go straight in the presence of air resistance. Straight trajectories are artificial and unnatural.
We know from the double slit experiment that light propagates as a wave anyway, bending in complex ways and not in straight line trajectories. Straight isn't the default there.
All Newton claimed is that objects will either remain at rest or continue to move at a constant velocity unless acted on by a force.
The examples you give are those of something being affected by a force.
We live in a world full of forces. So sure, if you don't steer a car it will not continue in a straight line (this is an example you give in the Wiki) because the tyres are on the road which is not perfectly flat and all kinds of frictional forces are being applied.
None of that refutes the statement that in the absence of a force it would continue at a constant velocity.
Now, light does bend of course in certain situations. We know about refraction and diffraction. Those don't apply to a light beam travelling through space although certain relativistic effects may.
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Where did Newton go to find no forces? Imagination land?
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Where did Newton go to find no forces? Imagination land?
It was his hypothesis. I guess based on the observations that things require a force to make them move or change direction.
And given that his theories have got us to the moon and are still used in many fields to make calculations they seem to have been pretty accurate and stood the test of time.
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So it is Imagination Land then. That just creates an assumption that there is a place where there are no forces.
Lets go into Imagination Land and try to get bodies to travel from Point A and Point B in a straight line.
Think of a rocket ship in space that blasts its engines for five seconds:
(https://i.imgur.com/Y4GueZj.png)
What makes you think it is possible to create an engine that fires perfectly evenly from all points? If the engine starts in the slightest manner from one side or gives off the slightest bit of more energy on one side then the rocket builds too much momentum on one side and goes spiraling off to one side, either quickly or slowly. It doesn't reach the Point B destination.
The only way to go straight is for the rocket to be constantly controlled and navigated. AKA, an artificial result.
Even in something as simple as the game of Pool, it is rather difficult to hit a ball to go straightly to the Point B hole:
(https://www.pooldawg.com/article/assests/Aiming_Straight_Shot.jpg)
You have to hit it in just the right spot to get it to go the way you want it to go. Luckily in pool you are only shooting a few feet.
What if you are shooting a ball at a Point B hole which is miles away? Ignoring the fact that you don't have the arm strength to do that, and ignoring everything about surface friction, to hit a pool ball perfectly for a distance ranging in miles and get into a hole is still very improbable. The ball is more likely to go off in some random direction.
So again, straight line trajectories between two points do not naturally occur in nature. They are highly unnatural.
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So it is Imagination Land then. That just creates an assumption that there is a place that there are no forces.
Even if we go into Imagination Land and think of a rocket ship in space that blasts its engines for two seconds:
(https://i.imgur.com/Y4GueZj.png)
What makes you think it is possible to create an engine that fires perfectly evenly from all points? If the engine starts in the slightest manner from one side or gives off the slightest bit of energy on one side then the rocket builds too much momentum on one side and goes spiraling off to one side, either quickly or slowly.
The only way to go straight is for the rocket to be constantly controlled. AKA, an artificial result.
There is a very simple way to make the rocket go straight.
Shut off the engine.
Now it's continuing to move, but any flaws in the engine no longer matter as it's not providing thrust.
It is now going straight, until acted on by an external force like the pull of gravity from a planet, or hitting an asteroid.
Analogies have limitations. A particle like a photon is very different than an active rocket engine or a car with wheels driving along the road. There are lots of things cars can do that photons don't.
Long range communications between all the planets we have visited, plus all the space probes that have been and currently are exploring the solar system are very good evidence that light and radio waves do indeed naturally travel in straight lines.
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Analogies have limitations. A particle like a photon is very different than an active rocket engine or a car with wheels driving along the road. There are lots of things cars can do that photons don't.
Light is pretty complex. There are several ways for light to bend. Here physicists bend light without applying any external force. Light bends on its own based on the properties of the phase of the beam.
https://physicsworld.com/a/light-bends-itself-round-corners/
Light bends itself round corners
Five years ago physicists showed that certain kinds of laser beam can follow curved trajectories in free space. Such counterintuitive behaviour could have a number of applications, from manipulating nanoparticles to destroying hard-to-reach tumours. But before this bizarre effect could be put to good use, researchers were faced with the challenge of how to bend the light through large enough angles to be useful. Now, two independent teams have solved this problem – and claim that the bending of sound and other kinds of waves could be next.
The concept of self-bending light was inspired by quantum mechanics and the realization in 1979 by Michael Berry and Nandor Balazs that the Schrödinger equation could support “Airy” wavepackets of particles, which accelerate without an external force. Then in 2007, Demetrios Christodoulides and colleagues at the University of Central Florida created the optical equivalent of an Airy wavepacket. This is possible because the equation describing paraxial beams – beams in which the constituent rays all travel almost parallel to the direction of the beam’s propagation – is mathematically identical to the Schrödinger equation once several parameters are interchanged, such as mass and refractive index.
The Florida team generated a specially shaped laser beam that could self-accelerate, or bend, sideways. The researchers did not bend the laser beam as a whole but rather the high-intensity regions within it. To do this they passed a centimetre-wide ordinary laser beam through a device known as a spatial light modulator that adjusted the phase of the beam at thousands of points across its width.
If light can do this, what makes you think that 'perfectly straight' would be the natural direction?
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Analogies have limitations. A particle like a photon is very different than an active rocket engine or a car with wheels driving along the road. There are lots of things cars can do that photons don't.
Light is pretty complex. There are several ways for light to bend. Here physicists bend light without applying any external force. Light bends on its own based on the properties of the phase of the beam.
https://physicsworld.com/a/light-bends-itself-round-corners/
Light bends itself round corners
Five years ago physicists showed that certain kinds of laser beam can follow curved trajectories in free space. Such counterintuitive behaviour could have a number of applications, from manipulating nanoparticles to destroying hard-to-reach tumours. But before this bizarre effect could be put to good use, researchers were faced with the challenge of how to bend the light through large enough angles to be useful. Now, two independent teams have solved this problem – and claim that the bending of sound and other kinds of waves could be next.
The concept of self-bending light was inspired by quantum mechanics and the realization in 1979 by Michael Berry and Nandor Balazs that the Schrödinger equation could support “Airy” wavepackets of particles, which accelerate without an external force. Then in 2007, Demetrios Christodoulides and colleagues at the University of Central Florida created the optical equivalent of an Airy wavepacket. This is possible because the equation describing paraxial beams – beams in which the constituent rays all travel almost parallel to the direction of the beam’s propagation – is mathematically identical to the Schrödinger equation once several parameters are interchanged, such as mass and refractive index.
The Florida team generated a specially shaped laser beam that could self-accelerate, or bend, sideways. The researchers did not bend the laser beam as a whole but rather the high-intensity regions within it. To do this they passed a centimetre-wide ordinary laser beam through a device known as a spatial light modulator that adjusted the phase of the beam at thousands of points across its width.
If light can do this, what makes you think that 'perfectly straight' would be the natural direction?
I think perfectly straight is natural because that is what we observe in nature. We send light and radio waves into space across vast distances to space probes and planetary landers and they have never been observed to bend. When we point our light and radio telescopes where we expect Mars to be, it's always there, as is the signals from the Mars rovers. If light was bending, we would notice Mars not being where it should, or radio signals from the rovers coming from unexpected directions.
The article you linked is interesting, but there is a note at the end.
However, Michael Berry of Bristol University in the UK, is less so. He believes that the authors do not make it clear that in their experiments they are not bending light rays themselves but the rays’ envelopes, or “caustics”.
It's an interesting effect to be sure, but I don't understand the process enough to really comment further on it yet. It certainly doesn't demonstrate 'natural' curving. I see no mention of this ever occurring in nature.
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So it is Imagination Land then. That just creates an assumption that there is a place where there are no forces.
Lets go into Imagination Land and try to get bodies to travel from Point A and Point B in a straight line.
Think of a rocket ship in space that blasts its engines for two seconds:
(You've just applied a force, then....)
What makes you think it is possible to create an engine that fires perfectly evenly from all points? If the engine starts in the slightest manner from one side or gives off the slightest bit of energy on one side then the rocket builds too much momentum on one side and goes spiraling off to one side, either quickly or slowly. It doesn't reach the Point B destination.
(So you design the engine with a gimbal, to vary it's direction of thrust, or add smaller subsidiary engines to direct the craft. All applying forces, so we're no longer in "no-force" land)
The only way to go straight is for the rocket to be constantly controlled and navigated. AKA, an artificial result.
(Or, set it off in the general direction of point B, and modify course as you approach. There is no obligation to complete all thrust and direction control at the start of the flight)
Even in something as simple as the game of Pool, it is rather difficult to hit a ball to go straightly to the Point B hole:
You have to hit it in just the right spot to get it to go the way you want it to go. Luckily in pool you are only shooting a few feet.
What if you are shooting a ball at a Point B hole which is miles away? Ignoring the fact that you don't have the arm strength to do that, and ignoring everything about surface friction, to hit a pool ball perfectly for a distance ranging in miles and get into a hole is still very improbable. The ball is more likely to go off in some random direction.
(Only due to forces acting upon it. Variations in the texture of the cloth surface below it. Billiard cloth has a direction to the woven fibres, the "nap" of the cloth. This affects how the ball behaves. Variations in the slate bed below the cloth. The table not being perfectly level. Wind. All apply force to the ball once it is on its way to the pocket.
So again, straight line trajectories between two points do not naturally occur in nature. They are highly unnatural.
Execute the pool shot on a surface of glass, ice, sheet metal or similar, and it will be far easier to get it to go straight
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What makes you think it is possible to create an engine that fires perfectly evenly from all points?
I don't think that. The craft that went to the moon did have to make occasional corrections.
In your analogy sure, if after the rocket fires the craft is not going along the line AB then the craft won't hit point B without correction.
That is not because it isn't going in a straight line, it's because it IS going in a straight line in the wrong direction.
You are basically asserting that the line AB is the only straight line which is obviously not correct.
Something going along a straight line - or let's put this in physics language, maintaining a constant velocity simply means the speed and direction of the rocket's path do not change without a force being applied.
This is an issue I have with your model of the sun's movements. It means a force will have to be constantly be applied to the sun to keep it moving in a circle and to keep changing the radius of the orbit. And to maintain a constant 24 hour circular period the sun would also have to keep increasing speed...and that increase in radius and speed would have to flip every 6 months so the radius and speed decrease. I don't believe any mechanism to make this happen has even been proposed.
What if you are shooting a ball at a Point B hole which is miles away? Ignoring the fact that you don't have the arm strength to do that, and ignoring everything about surface friction, to hit a pool ball perfectly for a distance ranging in miles and get into a hole is still very improbable. The ball is more likely to go off in some random direction.
Again, the fact the ball doesn't go in the pocket doesn't mean the ball isn't going straight. It just means it's going in the wrong direction.
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Interesting experiment for Tom's community proposal. What simple experiments would allow us to prove or disprove the hypothesis that light travels in straight lines (or nearly straight lines)?
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That is not because it isn't going in a straight line, it's because it IS going in a straight line in the wrong direction.
The rocket deviated from the straight line that was defined in the text as Point A to Point B. Therefore it's not going on the straight line. It's just one example that shows that there are too many variables to plan for in order to declare any particular trajectory to be the natural one, even if we use your hypothetical universe without external forces where Newton's laws hold.
If you want to get more real than that, radiation pressure from the craft would cause it to deviate further.
For the Pool Ball, any irregularities in the mass distribution in the ball would also manifest when rolling over miles.
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That is not because it isn't going in a straight line, it's because it IS going in a straight line in the wrong direction.
The rocket deviated from the straight line that was defined in the text as Point A to Point B. Therefore it's not going on the straight line.
It's going on a different straight line.
If the marksman aims rifle A at the bullseye B on the target, but someone nudges him as he pulls the trigger, the bullet still goes straight, but straight toward another point on the target, which we can call C.
The fact that the bullet misses B is not a proof of a bendy flight path, it's proof that the aim was adrift in the first place.
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Sure, but I am talking about straight line trajectories between two points:
So again, straight line trajectories between two points do not naturally occur in nature. They are highly unnatural
The (deep space) marksman would have been trying to hit his target. But if he can't hit his target for some physical reason, then his bullet didn't travel on the straight line. If you are trying to shoot straight and narrow through your sights, and you can't, then you didn't shoot straight and narrow.
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That is not because it isn't going in a straight line, it's because it IS going in a straight line in the wrong direction.
The rocket deviated from the straight line that was defined in the text as Point A to Point B. Therefore it's not going on the straight line.
Correct, it's going in a different straight line at a constant speed, just as Newton claimed.
It's not going along the line you defined but so what? You just defined an arbitrary line. There is no "the" straight line.
If the engine fires so the rocket is going along the line AB then when the engine stops the rocket will continue to point B at a constant speed unless any other forces act on it.
If the engine actually pushes the rocket in a slightly different direction then it will be going along a line AC instead, where C is some other arbitrary point.
In that case when the engine stops the rocket will continue to point C at a constant speed unless any other forces act on it.
That's all Newton's law claims.
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The (deep space) marksman would have been trying to hit his target. But if he can't hit his target for some physical reason, then his bullet didn't travel on the straight line. If you are trying to shoot straight and narrow through your sights, and you can't, then you didn't shoot straight and narrow.
You understand that the sun isn't "aiming" photons at the earth or moon or anything else, right?
Photons just leave the sun in every direction. Some of those will hit the earth if they're going in the right direction. Some will hit the moon and so on.
You seem to be conflating the ability to aim things perfectly in a certain direction with the assertion that once something is going in a certain direction at a certain speed then it will continue to do so unless acted on by a force. The second of these things is what Newton claimed, the first is neither here nor there.
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That is not because it isn't going in a straight line, it's because it IS going in a straight line in the wrong direction.
The rocket deviated from the straight line that was defined in the text as Point A to Point B. Therefore it's not going on the straight line.
Correct, it's going in a different straight line at a constant speed, just as Newton claimed.
It's not going along the line you defined but so what? You just defined an arbitrary line. There is no "the" straight line.
If the engine fires so the rocket is going along the line AB then when the engine stops the rocket will continue to point B at a constant speed unless any other forces act on it.
If the engine actually pushes the rocket in a slightly different direction then it will be going along a line AC instead, where C is some other arbitrary point.
In that case when the engine stops the rocket will continue to point C at a constant speed unless any other forces act on it.
That's all Newton's law claims.
My point is that Newton's assumptions are not really applicable in a real scenario. If the goal is to hit something to go to a destination we can't even rely on that.
From a Google Image Search on Newton's first law:
(https://mammothmemory.net/images/user/base/Physics/Newtons%20laws%20of%20motion/5.-an-object-at-rest-stays-at-rest.087493d.jpg)
There are so many variables here. Angle of the hit, mass distribution in the puck, friction of the ice. It is more realistic to say that the more variables added into any scenario, the less Newton's laws alone applies. If we believe that the universe doesn't provide Newton's perfect environment and perfect assumptions, then we can't really rely on your statement about "Newton said..."
You understand that the sun isn't "aiming" photons at the earth or moon or anything else, right?
Photons just leave the sun in every direction. Some of those will hit the earth if they're going in the right direction. Some will hit the moon and so on.
You seem to be conflating the ability to aim things perfectly in a certain direction with the assertion that once something is going in a certain direction at a certain speed then it will continue to do so unless acted on by a force. The second of these things is what Newton claimed, the first is neither here nor there.
There are some problems with that:
- Newton was wrong about his straight line particle propagation theory of light (See: Double Slit Experiment). It propagates as a wave.
- It assumes that space is perfectly homogeneous:
https://web.archive.org/web/20200811195324/http://www.tedpavlic.com/post_phil101_uncertainty.php
Author: Dr. Theodore P. Pavlic - http://www.tedpavlic.com/facjobsearch/docs/tpavlic_cv.pdf
Now, the more modern view of quantum mechanics treats photons as particles which carry a probability with them which has both a magnitude and a phase. When photons with equivalent magnitudes and opposite phases "intersect," their probabilities subtract to zero and no photon is detected. Keeping this in mind, understand that light does not travel in straight lines from one point to another. Light travels in all directions through all possible curves and paths from one place to another. In the end, our observations are of where the probabilities "add up," which typically is along a path of a straight line. When light is forced through inhomogeneous space its probabilities cancel in such a way where the curved paths add up or perhaps multiple paths show up.
https://web.archive.org/web/20200811195321/http://www.wlym.com/archive/pedagogicals/light.html
Author: https://www.genealogy.math.ndsu.nodak.edu/id.php?id=43126
Let's try to take on a Newtonian with this:
"So you see, light does {not} travel in straight lines!"
"Yes it does, if you do not disturb it. But by interposing matter, an inhomogenous medium, you deflected the rays from their natural, straight-line paths."
"How do you know that straight-line paths are `natural`?"
"If a light ray were allowed to propagate unhindered, in a pure vacuum or perfectly homogeneous medium, then it would propagate precisely along a straight line. It is just like the motion of material bodies in space according to Newton's first law: `a material body remains in its state of rest or uniform motion along a straight line, unless compelled by forces acting upon it to change its state.` No one could deny that."
"Does a `pure vacuum` exist anywhere in nature? Does a `perfectly homogenous medium' exist in nature?"
"Well no, of course. There is always a bit of dirt around, or inhomogeneities that disturb the perfectly straight pathways."
"So the presence of what you call `dirt` is natural, right?"
"Yes."
"So then it is natural that light never travels in straight-line paths."
"Wait a minute. You are mixing everything up. I am talking about the natural propagation of light, quite apart from matter."
"What do you mean, `quite apart from matter`? Do you assume that the existence of light is something that can be separated from the existence of matter?"
"Yes, certainly. The natural state of light is that of light propagating in a Universe that is completely empty of matter."
"And a completely empty Universe is a natural thing? Do you claim such a thing could ever exist?"
"I could imagine one. Sometimes I get that feeling inside my head."
"Maybe that is because you are not thinking in the real world."
"Don't blame me for that. I am a professional physicist."
"Well then, fill the vacuum in your mind with the following thought: Light and matter do not exist as separate entities, nor does matter act to bend rays of light from what you imagine in your fantasy-universe to be perfectly straight-line rays."
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That is not because it isn't going in a straight line, it's because it IS going in a straight line in the wrong direction.
The rocket deviated from the straight line that was defined in the text as Point A to Point B. Therefore it's not going on the straight line.
Correct, it's going in a different straight line at a constant speed, just as Newton claimed.
It's not going along the line you defined but so what? You just defined an arbitrary line. There is no "the" straight line.
If the engine fires so the rocket is going along the line AB then when the engine stops the rocket will continue to point B at a constant speed unless any other forces act on it.
If the engine actually pushes the rocket in a slightly different direction then it will be going along a line AC instead, where C is some other arbitrary point.
In that case when the engine stops the rocket will continue to point C at a constant speed unless any other forces act on it.
That's all Newton's law claims.
My point is that Newton's assumptions are not really applicable in a real scenario. If the goal is to hit something to go straight to a destination we can't even rely on that.
From a Google Image Search on Newton's first law:
(https://mammothmemory.net/images/user/base/Physics/Newtons%20laws%20of%20motion/5.-an-object-at-rest-stays-at-rest.087493d.jpg)
There are so many variables here. Angle of the hit, mass distribution in the puck, friction of the ice. It is more realistic to say that the more variables added into any scenario, the less Newton's laws alone applies. If we believe that the universe doesn't provide Newton's perfect environment and perfect assumptions, then we can't really rely on your statement about "Newton said..."
There is nothing wrong with Newton's laws applying to the real world. He says that without any external forces acting on an object it will continue it's current motion, which is true.
You are right that a hockey puck has plenty of external forces acting on it. Variations of friction on the ice, air currents, the hockey stick not being perfectly flat. But why are any of those a problem for Newton? In the end, we humans have intelligence and free will and can pick up that hockey puck at any time. So no laws could describe it's motion ever because we can always intervene. But Newton's laws still work and are useful, and in the case of picking it up, we still use them.
We can also still use Newton's laws to send spacecraft to Mars and Pluto. We can still send and receive radio signals that go straight from Earth to them. We can still see the planets they orbit or landed on with telescopes, again with straight lines. If they were not straight they wouldn't match Newton's predictions of their locations. We rely on Newtons laws for a large number of things, including all the satellites in orbit. We very much rely on them, and very applicable in a real scenario.
The real world is complicated and has lots of variables, but if you account for enough variables you can get your predictions as accurate as you need. A hockey player doesn't need to worry about micro-air-currents when he's 10 feet in front of the goal and trying to get the puck past the goalie. There are a million small variables at play, but he doesn't need to know about most of them. He doesn't know the exact temperature of the puck or the ice, but he can still hit it where he wants.
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Even if we only look at the internal variables, if the the mass distribution in a puck isn't perfect, then one side of it has more momentum than the other. That would cause a curved route.
Image:
(https://i.imgur.com/wJKo2bF.png)
In a hockey game the puck is likely always curving slightly by some internal or external variable. And manufacturers try to keep the mass in pucks as symmetrical as possible.
Hockey pucks are also unnatural artificial constructs. If we think of something natural like a rock, those are likely to have more mass distribution discrepancies.
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Even if we only look at the internal variables, if the the mass distribution in a puck isn't perfect, then one side of it has more momentum than the other. That would cause a curved route.
Image:
(https://i.imgur.com/wJKo2bF.png)
In a hockey game the puck is likely always curving slightly by some internal or external variable. And manufacturers try to keep the mass in pucks as symmetrical as possible. Hockey pucks are unnatural artificial constructs. If we think of something natural like a rock, those are likely to have more mass distribution discrepancies.
I still don't see the problem here.
Nothing about hockey pucks not having perfect mass distribution invalidate Newton's laws, or make those laws impossible to use in the real world.
No matter what theory anyone comes up with, the real world will be messy and have lots of variables. A hockey puck is going to be imperfect on a round or flat Earth, imperfect using Newton's laws or any replacements. Hockey players can still hit them into a net, and we can still use Newton's laws to land robots on Mars and send spacecraft to Pluto and beyond. Clearly all these discrepancies are not a problem or every hockey game would be 0-0 and we wouldn't have pictures of other planets from close up.
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Hockey players can still hit them into a net
It takes practice and skill to become good at hockey. You are describing an intelligent process with your analogies, not nature.
Aiming, controlling, keeping something on course, are all artificial acts of man, and unrelated to whether straight line trajectories between points are or are not natural.
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Hockey players can still hit them into a net
It takes practice and skill to become good at hockey. You are describing an intelligent process with your analogies, not nature.
Aiming, controlling, keeping something on course, are all artificial acts of man, and unrelated to whether straight line trajectories between points are or are not natural.
Just so I understand, Tom, do you agree with the standard claim that momentum p is a vector quantity and equal to mv, where m is mass, and v is a vector, i.e. a speed in a specific direction? Obviously all objects have forces acting upon them, and so their momentum will change all the time. Is that your point?
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Hockey players can still hit them into a net
It takes practice and skill to become good at hockey. You are describing an intelligent process with your analogies, not nature.
Aiming, controlling, keeping something on course, are all artificial acts of man, and unrelated to whether straight line trajectories between points are or are not natural.
You were the one who brought the hockey analogy into the argument, and the spaceship with controlled thrust.
I agree with you completely that artificial acts of man have nothing to do with how objects move in nature, and are unrelated.
What we observe, is photons and planets and objects dropped on Earth all obey Newton's laws. Light travels straight from here to Pluto, arriving exactly where it should. We know how light behaves, we can account for everything that reflects, refracts or pulls on it via gravity.
We assume light and objects move in straight lines unless otherwise acted upon because that is what we observe.
If someone spots light spiraling or curving or bending in ways that break the laws of physics as we know it, that will be an exciting day.
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So it is Imagination Land then. That just creates an assumption that there is a place where there are no forces.
Lets go into Imagination Land and try to get bodies to travel from Point A and Point B in a straight line.
Think of a rocket ship in space that blasts its engines for five seconds:
(https://i.imgur.com/Y4GueZj.png)
What makes you think it is possible to create an engine that fires perfectly evenly from all points? If the engine starts in the slightest manner from one side or gives off the slightest bit of more energy on one side then the rocket builds too much momentum on one side and goes spiraling off to one side, either quickly or slowly. It doesn't reach the Point B destination.
The only way to go straight is for the rocket to be constantly controlled and navigated. AKA, an artificial result.
Even in something as simple as the game of Pool, it is rather difficult to hit a ball to go straightly to the Point B hole:
(https://www.pooldawg.com/article/assests/Aiming_Straight_Shot.jpg)
You have to hit it in just the right spot to get it to go the way you want it to go. Luckily in pool you are only shooting a few feet.
What if you are shooting a ball at a Point B hole which is miles away? Ignoring the fact that you don't have the arm strength to do that, and ignoring everything about surface friction, to hit a pool ball perfectly for a distance ranging in miles and get into a hole is still very improbable. The ball is more likely to go off in some random direction.
So again, straight line trajectories between two points do not naturally occur in nature. They are highly unnatural.
Ok, so you don't believe in straight line trajectories. So this leads to the question, how can we measure anything?
How do we know that the light reflected from the ruler we just measured the length of something as 20 centimeters or whatever, isn't nature just playing tricks on us?