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Watsisname
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03 Nov 2020 01:24

OK, so you're basically saying that it all boils down to Einstein's insight that there is no universal time, no way to peel space and time apart, no fixed reference for either can be established?


Pretty much! Space and time are deeply interwoven, and one of its many consequences is that it is fundamentally impossible to measure the one-way speed of light. It becomes a sort of circular logic: to measure the one-way speed of light, one must first know the one-way speed of light, because the very method of measuring it in one direction requires knowing the time at multiple locations, which requires a method of synchronizing clocks, which requires using the speed of light. Many people have tried to devise experiments to get around this, but all end up only measuring the two-way speed of light. Even with such clever ideas as using signals from GPS satellites.

This is intimately connected to the relativity of simultaneity, because any given two-way synchronization scheme will not actually achieve synchronization in all frames, and a one-way synchronization scheme is ambiguous. Why? Well, what time is it on Mars right now? It's a meaningless question. If Mars is 20 light minutes away, then what we might consider simultaneous events on Earth and Mars may be seen 20 minutes apart in another frame, and with either event happening first! The best we can do is agree to a synchronization scheme where a signal travels both ways. That is the only way we can know our clocks are actually synchronized according to our own inertial frame.

Does it mean that it's ultimately a convention when we say that the distance from A to B is equal to the distance from B to A?

Indeed! Once we accept that the one-way speed of light is unknowable (though can't be less than c/2 in any direction), the one-way distance between points in space is also unknowable. Even the very definition of a meter makes no sense in one direction, because it's defined by the two-way speed of light. 

What does it mean to measure the distance between two points? In relativity, we mean the proper distance, which is that in which the spatial location of the two ends is measured instantaneously by observers who are in an inertial frame in which both points are at rest. But to set up this inertial frame and make an instantaneous measurement of positions, we need to synchronize clocks!  Doh!

Is this making more sense, or weirding you out even more? :P  Hang in there, because my next post might just blow your mind.
 
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03 Nov 2020 04:11

midtskogen wrote:
Source of the post Centuries ago one could, I suppose, argue that we couldn't know that the orbits actually didn't slow down or speed up and the speed of light varied depending on the direction, but today we can have probes around Jupiter and Saturn observing the moons.  Meanwhile on Earth we observe the transits and occultations of the moons accurately and we get reports from the probes that, no, the orbits did not change despite what we observed.  Therefore the one way speed of light did not change with direction, only our distance to the planets.


That the one-way speed of light (and from now on I will simply say "the speed of light" to mean the one-way speed of light, and say two-way speed of light otherwise) is immeasurable is something I did learn briefly during a special relativity course, which blew my mind as much as Derek's and everyone else's, but along with much else that we learn in relativity it eventually became somewhat comfortable. However, I had never seen nor tried to prove why certain attempts to measure it would fail except for some really simple ones like what Veritasium walked through so elegantly.

Your thought experiment of using orbital motion is a great one, because it is very tempting to think that even if satellite motion is actually nonuniform in such a way that one observer sees it as uniform with an anisotropic speed of light, that a different observer would not see it uniform, and so the effect should still be observable.

Why doesn't this work?

Now, I've never seen this shown, and to be honest I was not certain about it. I simply believed very strongly that it must fail somehow. So when I answered by saying "ah, but what are the laws of motion with an anisotropic speed of light?", I was hinting that it is conceivable that the laws of motion could be different in such a way that the effect is not noticeable. In other words this is not really a measurement, but rather an argument that the observed uniformity of orbital motions implies an isotropic one-way speed of light. But unless we prove that there is no alternative self-consistent picture of orbital motion with anisotropic light, or unless we prove that there is at least one which is, then the question of whether this experiment works lies unresolved.

So... let's actually calculate this! I've coded something up to do just that, and the result blew my mind all over again, because while I expected this result, I had trouble really believing it.

Methodology:
Let's consider a satellite in a circular orbit about the origin. I think it's intuitive that if the speed of light depends on direction, then if the true satellite motion is uniform, an observer at the origin will see it be nonuniform. Of course, we know circular motion does appear uniform from the origin, so it must be the case that the true motion is nonuniform if the speed of light depends on direction. The critical question: what will that motion be, in order for the observer to see it as uniform?

To find out, I calculate it somewhat backwards. Imagine you are sitting at the origin with a laser pointer, and you swivel it around by rotating at a constant angular speed. If the speed of light is isotropic, the laser's intersection with the satellite's orbit will be in uniform circular motion as well. But if the speed of light is anisotropic, then the intersection will move non-uniformly, and in exactly the right way as to match (in reverse) what the motion of the satellite must be so that the satellite appears to be moving uniformly according to the origin. 

So by computing the time of intersection of the laser with the orbit, we can find where the satellite must be so that it appears to move uniformly, at least according to the origin. But what will another observer at different arbitrary location see? Surely they can't also see the satellite move uniformly, can they?

In fact, they don't. But neither would they if the speed of light was actually isotropic, and the motion actually uniform. After all, when the satellite is closer to the observer, the light travel time is shorter. And here's the catch. If they assume that the speed of light is isotropic, and compensate for the light travel time from where they see the satellite to be, then they will say the true motion of the satellite is perfectly uniform!  


Proof (sort of):
We need a function describing the speed of light as a function of direction. We know the most extreme case is that it could move at c/2 one way and infinitely fast in the other. For fun, let's choose that. But for this problem we need to know the speed in all directions in the 2D plane. There are infinitely many functions of direction we could choose that would satisfy c/2 one way and infinity the other way, but in order to be consistent with relativity, we need the two-way speed of light to be c in all directions. This forces a condition on our function, and its harmonic mean in opposing directions must be equal to c.

Which function has this property? Thankfully, this work is already done for us by Iyer and Prabhu who derive it for the three dimensional case in this paper (see equation 39). We can easily adopt to our two dimensional case. The function is:

Image


where in our choice of most extreme anisotropy we will let v/c = 1, which gives a maximum of c' of infinity for light moving in the upward direction (toward θ=pi/2), and a minimum of c'=c/2 for light moving in the downward direction (toward θ=3pi/2). And for a quick consistency check, if we look at the opposing directions pi/4 and 5pi/4, the one-way speeds (in units of c) are 2 - sqrt(2) and 2 + sqrt(2), respectively, and their harmonic mean is 1.

Here's the plot for when the light from the satellite reaches different observers. I set c=1 (we can always choose units where this is true, like 1 light year per year), a circular orbit at 10 light seconds, which appears from the origin to be in uniform motion at a speed of c/2. The yellow curve indicates the perceived motion of the satellite from the origin, while the blue curve indicates the true motion of the satellite. (All motion here is counterclockwise, in the direction of increasing angle.)

Image


Notice that in order for the origin to see uniform circular motion, the satellite must be moving the fastest (curve is shallowest) at θ=0°. Then we see the greatest delay between true position and perceived position at θ=90°, which is the direction from which light travels the slowest. Makes sense. The satellite then accelerates, reaching its maximum true speed at θ=180°, and then its true position equals its apparent position at θ=270°, which makes sense because that is the direction from which light travels instantly, and the origin sees the satellite "in real time".

So far so good. Next I compute the time for the light to reach another observer located on the orbit in the direction of 180°, and add that to the plot with a thin white line. This represents where that observer sees the satellite.

Finally, I compute what this observer would see from a satellite undergoing circular motion with same angular speed that the origin sees, and assuming light moves at c in all directions. That is the thick dashed white curve.

Image


Voilà! The curves are exactly the same. Also what's important here is not that they overlap, but have the exact same shape. (This assertion might be difficult to swallow -- if so, think about the Einstein synchronization convention, or check the last sentence of the abstract of Iyer and Prabhu's paper.) Hence, both the origin and the observer at another location think the satellite is undergoing the same uniform circular motion, even though the satellite is not in uniform motion at all! Nature conspires to make this effect, and hence the one-way speed of light, utterly unobservable


Image


Is this a wacky coincidence of my choices for the orbital radius, speed, or observer location?  No. You may feel free to play with the code. :)

# -*- coding: utf-8 -*-
"""
Created on Sun Nov  1 18:46:20 2020
@author: Watsisname
"""

import numpy as np
import math
from matplotlib import pyplot as plt

pi = np.pi          #define pi

c=1                 #set the speed of light. Suggest setting c=1
r=10                #set the radius of the circular orbit.    
beta = 0.5          #set the velocity of the orbit (in units of c) 
v = beta*c          #convert to normal units (if c != 1)
period = 2*pi*r/v   #calculate the orbital period
freq = 1/period     #calculate the orbital frequency
w=2*pi*freq         #calculate the angular frequency

"""
In this first code block we will calculate the true (nonuniform) motion of the satellite such that
an observer at the origin will see it undergo apparently uniform circular motion. We will do this backwards.
Imagine the origin is a laser rotating opposite the direction the satellite is orbiting, in uniform motion.
What we will do is use the nonisotropic speed of light and calculate when this laser will intersect
the satellite orbit at a particular angle. That time then will correspond to when the satellite should 
be at that position, such that its motion appears uniform at the origin.
"""

theta = np.arange(0, 2*pi, .001)     #create a list of angles from 0 to 2pi
t_emit = (theta - 2*pi)/w            #calculate the time at which the origin emits light in the direction theta

#Define the expression for the one-way speed of light. To be consistent with relativity, the formula must 
#have a harmonic mean of c. That is, the two-way speed of light in all directions must be c.
c_theta = c/(1+np.sin(theta))
                
tau_theta = r/c_theta                #calculate the travel time for the light to reach the orbit from the origin
t_arrive = t_emit - tau_theta        #calculate the arrival time of the light at the orbit.

offset = t_arrive[0]                 #the computed times will start out negative, so let's apply an offset so time starts at 0
t_arrive = t_arrive - offset
t_emit = t_emit - offset

"""
In this next block, we will place an observer at coordinates (x_obs, y_obs), and calculate what they will see
the satellite's motion to be (using its actual non-uniform motion calculated above and the anisotropic one-way
speed of light), and then compare it with what they expect if the true motion was uniform and there was no anisotropy.
"""


x_obs = -r                           #x component of observer
y_obs = 0                            #y component of observer
dx = x_obs - r*np.cos(theta)         #x component of sat-obs distance
dy = y_obs - r*np.sin(theta)         #y component of sat-obs distance
a = np.sqrt(dx**2 + dy**2)           #distance from satellite to observer

theta_obs = []                       #calculate the angle from satellite to observer
for i in range(0,len(dx)):
    theta_obs.append(math.atan2(-dy[i],-dx[i]))
    

for i in range(0,len(theta_obs)):                   #apply a shift so that negative angles are positive (from 0 to 2pi)
    if theta_obs[i] < 0:
        theta_obs[i] = theta_obs[i] + 2*pi
theta_obs = np.array(theta_obs)                     #convert list to array

c_theta_obs = c/(1+np.sin(theta_obs))               #calculate the speed of light from satellite to observer
tau_obs = a/c_theta_obs                             #calculate the light-travel time from satellite to observer
t_obs = t_arrive + tau_obs                          #calculate the time at which the light reaches the observer

"""
Finally we will calculate what the observer *would* see if the satellite was actually undergoing the same uniform
circular motion that an observer at the origin sees, and assuming an isotropic one-way speed of light. What we want
to check is whether these match or not. If they match, then it means the one-way speed of light is not measurable by
watching orbital motion, because orbital motion will be nonuniform in exactly the right way to cancel the light-travel
time effects for all observers!
"""
tau_c_obs = a/c                            #calculate the sat-obs travel time as if lightspeed is isotropic
t_c_obs = theta/w + tau_c_obs              #calculate the arrival time of the light as if the satellite was in uniform motion


#This plots the one-way speed of light vs. the direction it is moving."
fig0, ax = plt.subplots(1,1)
ax.plot(theta*180/pi, c_theta, '-k', linewidth=2)
fig0.suptitle('A Nonisotropic Speed of Light: one-way speed vs. direction', size=10)
fig0.set_figheight(6)
fig0.set_figwidth(6)
fig0.set_dpi(120)
ax.set_xlim(0, 360)
ax.set_ylim(0, 6)
ax.set_xlabel('direction of light ray propagation [degrees]')
ax.set_ylabel("speed of light [in units of c]")
plt.grid(which='major')
plt.figure(figsize=(10,12))


#This plots the arrival time of the light from the satellite for each observer.
fig1, ax = plt.subplots(1,1)
ax.plot(theta*180/pi, t_arrive, '-r', linewidth=1, label='true motion of satellite')
ax.plot(theta*180/pi, t_emit, '-b', linewidth=1, label='where origin sees satellite')
ax.plot(theta*180/pi, t_obs, '-k', linewidth=1, label='where observer sees satellite')
ax.plot(theta*180/pi, t_c_obs, '--k', linewidth=2, label="expectation assuming isotropy")
fig1.suptitle('An Anisotropic One-way Speed of Light: \n Satellite in nonuniform circular orbit at r=10, such that \n origin sees uniform speed c/2, and observer is located at (x,y) = (-r,0)', size=10)
fig1.set_figheight(6)
fig1.set_figwidth(6)
fig1.set_dpi(120)
ax.set_xlabel('angular position of satellite [degrees]')
ax.set_ylabel("time in book-keeper's frame [r/c]")
plt.grid(which='major')
ax.legend(loc=4)
plt.figure(figsize=(10,12))
 
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midtskogen
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03 Nov 2020 05:49

Great job with your posts.  This is a deep rabbit hole.
Watsisname wrote:
Source of the post Nature conspires to make this effect, and hence the one-way speed of light, utterly unobservable. 

It needs to sink in a bit.  But if a mathematical proof of the isotropy is doomed to be forever elusive, what about a more philosophical approach - is there a valid argumentum ad absurdum?  That is, showing that assuming anisotropy leads to a contradiction or something that cannot be true.  But special relativity can't be used since it already assumes isotropy.

We're left with all the confirmations of relativity, which is strong evidence for isotropy, but not a proof... But this is not an issue if you have accepted that absolute truth is always elusive, that we can only establish holistic truths are don't involve any contradictions.
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03 Nov 2020 14:16

That was awesome. What an incredible insight on the topic. Thanks Watsisname. You never dissapoint.
 
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04 Nov 2020 15:05

Thanks Dr Wat ;-) is the cosmic censorship theorem also part of nature conspiring against us so we cant see naked singularities?  Perhaps this too is a property of the universe, without which the universe would have a "hole" in it that would cause it to deflate?

I have a question for you about the elementary nature of space and time.  I realize we may not know the answer to this without a fully working theory of quantum gravity.  But do you think that space and time are fundamental in nature or do they give way to some underlying principles on the subplanck scale?  Quantum mechanics seems to break many of the rules of Relativity and perhaps this is because space and time aren't fundamental and even more to the point, perhaps space-time isn't a continuum but consists of discrete units, which would be a way for singularities not to happen (which, pardon the pun again, are a hole in relativity)- if the smallest units had a discrete length, then infinite density could not occur.

By the way this paper is excellent and brings me back to my college days 
https://arxiv.org/ftp/arxiv/papers/1001/1001.2375.pdf
Back then I just accepted this without thinking too deeply about it, but then I realized that the "speed of light" is MUCH more than just the "speed of light"- it is a basic property of the universe with which everything else is measured against.  It is the standard which does not vary (in a vacuum).  And there is no way to measure the one way speed of light because to do so would mean breaking one of the fundamental laws of the universe. 
 
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04 Nov 2020 23:09

Nature is also "conspiring" against time travel, but the paradoxes in that case are easier to see.
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05 Nov 2020 23:37

Watsisname wrote:
Source of the post Proof (sort of):

Now I will go back and make the proof a bit more formal. While looking at specific circumstances with the code above was compelling and probably easier to visualize and follow than a derivation full of equations, I'd still like to show by algebraic means that the effect of an anisotropic speed of light is not observable in orbital motion, for all observers. I will also prove it for all ranges of anisotropy (not just c/2 one way and infinity the other, but for any values in between).

An even more impressive thing will pop out of this at the end, too, which is the asynchronization of clocks (the relativity of simultaneity). By that I mean that different observers will believe that their clocks are synchronized according to Einstein's synchronization convention, but "in reality" they may not be. This also fleshes out something I had left a bit vague at the end of the prior post. As a quick refresher, refer to Veritasium's video at 13:49, when he shows the flexibility on the spacetime diagram for where "now" is for Mars.

The ultimate goal of this post is really to make the relativity of simultaneity come out of the shadows, and into plain view. :)

Let's get started.

As before, the formula describing the one-way speed of light vs. direction is

Image

where vb is a sort of "boost" indicating how much the speed of light is anisotropic. A boost of vb=c will result in the maximum allowed anisotropy. In this case I'm going to treat theta as the direction the light is moving towards rather than from. This won't change the physics, it just means I've flipped the coordinate system, or the direction of anisotropy, around.

What we seek is an expression for the true motion of a satellite with anisotropic speed of light, such that an observer at the origin sees it undergoing the same uniform circular motion that they expect under an assumption of an isotropic speed of light. The time at which the origin must see the satellite at an angle theta is

Image

where r is the radius of the satellite's circular path, ω0 is its angular velocity, and of course c is the two-way speed of light. 
If the speed of light is anisotropic according to the first equation, then the light from the satellite actually reaches the observer from the direction theta at the time (measured by a clock at the origin),

Image

where tsat(theta) represents the true motion of the satellite (which we want to find), τ represents the light's travel time from satellite to origin, and the expression for c' has a shift of 180° because now we want to know the speed at which light moves from the theta direction to the origin.
 Plugging in what we know,

Image

and rearranging,

Image

we find the true satellite motion must be

Image

Notice this expression is not solvable analytically for the angular position theta in terms of time. Keeping it in terms of time vs. angle is actually simpler, as well as more convenient for plotting things on a spacetime diagram where time is the vertical axis. And we've already seen an example of what this motion may look like (an oscillation from uniform motion like the blue curve in the last post).

Okay, now we want to find the satellite motion that will be observed by an observer at any location in space. Let their location be (x,y) with respect to the origin, the distance from satellite to observer be a, and the angle from satellite to observer be ϕ. Then the time at which light from the satellite reaches the observer is

Image

Whereas if the speed of light is isotropic, and the true satellite motion is uniform, then this would be

Image

We're almost there. What we want to do is find out what condition would allow these two descriptions of the satellite motion measured by the observer to be exactly identical. We want to see if there is a consistent physics where nonuniform circular motion with an anisotropic speed of light looks indistinguishable from uniform circular motion with an isotropic speed of light.

So, set these two expressions for the observer's view of the satellite to be equal to each other. However, there is one assumption that we must deliberately not make. Let us not assume that the observer's clock is in sync with the origin's clock. Remember that if the speed of light is anisotropic, then the Einstein synchronization convention will not guarantee the clocks are truly synchronized. So, to the expression for observer time in the anisotropic perspective, let's add an unknown time-shift, Lambda (Λ).

Image

The uniform angular motion term θ/ω0 appears on both sides, so it cancels, and expanding the parentheses out we have

Image

Now the light travel time terms a/c cancel, and from looking at the trigonometry, we can identify sin(ϕ) as the difference between y coordinate of observer and satellite divided by the distance between them, which is equal to y-rsin(θ) divided by a.

Image

Now let's expand this out and bring everything except lambda to the other side,

Image

finally, the 2nd and 3rd terms cancel, leaving

Image

What a simple, beautiful result this is! Can you see its significance? 

This is saying that in order for all observers to see the same apparent uniform circular motion of an object with an anisotropic speed of light, the true satellite motion must be nonuniform, and clocks must be out of sync with each other, proportionally to their displacement along the axis of anisotropy (in this case the y axis), and depending on the magnitude of the anisotropy, according to -vb/c2.  

This is the relativity of simultaneity, staring us in the face!

If you've ever seen that problem in special relativity of two clocks on a train, one at the front and back, then if they are synchronized according to those on the train, they will not be synchronized according to people standing next to the track. The extent to which they are out of sync, in terms of seconds per meter along the train, follows this same expression. It arises from the transformation between frames, which is also like changing the one-way speed of light between frames.

Think again back to the Veritasium video with the attempt of synchronizing clocks on Earth and Mars. If they are 10 light minutes apart, and if the speed of light is c/2 towards Mars and infinitely fast back to Earth, then Einstein's synchronization convention will result in Mars' clocks lagging the Earth's clocks by 10 minutes. That's exactly what this result here is showing us, too! Let the boost be c for maximum anisotropy, let Mars' distance be y=10 light minutes in the direction that the one way speed is c/2, and we get a time difference on Mars of -10 minutes!

As Veritasium said, this asynchronization cannot be known, and likewise the "true" one-way speed of light is unknowable. It won't show up in any method of comparing signals or time measurements, and it doesn't even show up in the apparent motions of celestial bodies. So because this is unknowable and doesn't change any of the physics, then by choice, we say the one-way speed of light is the same in all directions, because it makes things the most simple.

"It can scarcely be denied that the supreme goal of all theory is to make the irreducible basic elements as simple and as few as possible without having to surrender the adequate representation of a single datum of experience.” -- A. Einstein



By the way, you might have wondered what this must mean for our motion here on Earth. We're orbiting the Sun in (almost) uniform circular motion. But if light is anisotropic then we should be experiencing some anomalous speeding up and slowing down even if the orbit was perfectly circular. Why don't we notice it? Could we notice it? No. It could be cancelled perfectly by an additional time dilation effect for our clocks. With a pinch of calculus we can find the time dilation formula along the orbit:

Image
 
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06 Nov 2020 01:56

midtskogen wrote:
Source of the post But if a mathematical proof of the isotropy is doomed to be forever elusive, what about a more philosophical approach - is there a valid argumentum ad absurdum?  That is, showing that assuming anisotropy leads to a contradiction or something that cannot be true.

Any proof by contradiction should be able to be stated mathematically as well, I think. For instance, Olber's Paradox is often described conceptually with a thought experiment, but it can be proved mathematically. Either way, I have not met any approach where by beginning with an anisotropic one way speed of light, a contradiction is reached. Instead, effects will perfectly mask it, and those effects ultimately have something to do with special relativity, just often in non-obvious ways.

midtskogen wrote:
Source of the post But special relativity can't be used since it already assumes isotropy.


Exactly. And consider that the asynchronization effect popped out of the math for making circular motion still appear uniform with aniostropic light, yet nowhere did I invoke relativity! My starting assumption was that the two-way speed of light must be isotropic, which is a measurable fact. I did not need to invoke the invariance of the spacetime interval, or the Lorentz transformations, or time dilation formulas, or any other results of relativity. Then I deliberately choose not to make any other unnecessary assumptions, like that orbital motion must truly be uniform, so that we could find and describe the effects that would lead to consistency, if consistency can exist.

Special relativity did it a slightly different way. It began with the isotropic (and invariant) two-way speed of light, and relaxed the assumptions of a universal time and space. It does assume that the one-way speed of light is isotropic, as a choice of method for synchronizing clocks. But as we saw, anisotropy of the one-way speed of light is not measurable, and consequences of isotropy being "wrong" don't lead to observable effects. So this really is a free choice in relativity, and I would say the one-way speed of light, while it has some kind of meaning (like, it can't be zero in any direction), is not of the same level of physicality as other quantities we can measure.
 
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06 Nov 2020 03:00

Whilst homogeneity and isotropy are reasonable, though unproven/unproveable, assumptions on the macroscopic scale, what about at quantum scale, or early universe scale?  Is there a need for this isotropy there, or could assuming anisotropy add any explanatory force at that level?  That would be interesting.  Could isotropy be simply be an emergent property of the quantum world?  It sounds a bit silly, but since relativity breaks down, is there something else that isotropy is needed for?
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08 Nov 2020 05:35

Those are some awesome points!  There is also the matter of the cosmic microwave background and "clumping" and other anomalies on that scale, which haven't been properly explained yet and were the main reason Penrose formulated his Conformal Cyclic Cosmology.

Also, it would be interesting to model the behavior of light in intense gravitational fields....for example do these rules break down inside black holes?  What about with regards to closed timelike curves surrounding spinning black holes?

Also- and I guess this is more of a philosophical or metaphysical question.....would it possible in the far future for humanity to break the geometry of the universe (let's say by creating micro black holes in collider experiments, or artificial traversable wormholes or both) and what would be the result if humanity were one day able to break relativity? Honestly, if I had unlimited funds, I would pay the top 1000 scientists on the planet to work 24/7 on this.  Someone else can find new energy sources or a cure to cancer or whatever, but breaking the laws of the universe or creating a new stable universe where those laws dont exist would be the ultimate human accomplishment.
 
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12 Nov 2020 20:14

midtskogen wrote:
Whilst homogeneity and isotropy are reasonable, though unproven/unproveable, assumptions on the macroscopic scale, what about at quantum scale, or early universe scale?  Is there a need for this isotropy there, or could assuming anisotropy add any explanatory force at that level?  That would be interesting.  Could isotropy be simply be an emergent property of the quantum world?  It sounds a bit silly, but since relativity breaks down, is there something else that isotropy is needed for?

You would like this
https://www..quantamagazine.org/quantum ... 0201020/#0
Quantum Tunnels Show How Particles Can Break the Speed of Light

Recent experiments show that particles should be able to go faster than light when they quantum mechanically “tunnel” through walls.
https://www..quantamagazine.org/quantum-tunnel-shows-particles-can-break-the-speed-of-light-20201020/#0
 
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midtskogen
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12 Nov 2020 23:16

A-L-E-X wrote:
Source of the post Recent experiments show that particles should be able to go faster than light when they quantum mechanically “tunnel” through walls.

Well, in the quantum world violations of the laws physics, stay in the quantum world.
NIL DIFFICILE VOLENTI
 
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13 Nov 2020 09:13

midtskogen wrote:
A-L-E-X wrote:
Source of the post Recent experiments show that particles should be able to go faster than light when they quantum mechanically “tunnel” through walls.

Well, in the quantum world violations of the laws physics, stay in the quantum world.

Indeed!  Although we can add black holes and the big bang/bounce to that list.  The reason why black hole singularities exist maybe is because they are macroscopic representations of the quantum world.  On the very fundamental quantum level, space, time and even causality may not exist, because like you said, they are aggregates of more fundamental, discrete quantities out of which they emerge.  The same can be said of the big bang/bounce singularity.  Quantum laws apply at that level rather than relativity.  I envision each universe as its own quantum particle/wave that expands inside the dimensions it creates for itself from within and the whole omniverse can be viewed as "cosmic quantum soup" that forever keeps bubbling with new universes that are either expanding or contracting cyclically, creating baby universes inside their own supermassive black holes, until they finally completely run down on the value of their own cosmological constant and die a slow death only leaving behind the baby universes they've created which themselves slowly run down with their own cosmological constants going down with each iteration of the cycle.
 
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14 Nov 2020 08:41

https://getpocket.com/explore/item/cosm ... ket-newtab

                                              One curious pattern cosmologists have known about for decades is that space is filled with correlated pairs of objects: pairs of hot spots seen in telescopes’ maps of the early universe; pairs of galaxies or of galaxy clusters or superclusters in the universe today; pairs found at all distances apart. You can see these “two-point correlations” by moving a ruler all over a map of the sky. When there’s an object at one end, cosmologists find that this ups the chance that an object also lies at the other end.

The simplest explanation for the correlations traces them to pairs of quantum particles that fluctuated into existence as space exponentially expanded at the start of the Big Bang. Pairs of particles that arose early on subsequently moved the farthest apart, yielding pairs of objects far away from each other in the sky today. Particle pairs that arose later separated less and now form closer-together pairs of objects. Like fossils, the pairwise correlations seen throughout the sky encode the passage of time — in this case, the very beginning of time.                                      

......

 “They’ve found ways of calculating things that just look totally different from the textbook approaches,” said Tom Hartman, a theoretical physicist at Cornell University who has applied the bootstrap in other contexts.

Eva Silverstein, a theoretical physicist at Stanford University who wasn’t involved in the research, added that the recent paper by Arkani-Hamed and collaborators is “a really beautiful contribution.” Perhaps the most remarkable aspect of the work, Silverstein and others said, is what it implies about the nature of time. There’s no “time” variable anywhere in the new bootstrapped equation. Yet it predicts cosmological triangles, rectangles and other shapes of all sizes that tell a sensible story of quantum particles arising and evolving at the beginning of time.

This suggests that the temporal version of the cosmological origin story may be an illusion. Time can be seen as an “emergent” dimension, a kind of hologram springing from the universe’s spatial correlations, which themselves seem to come from basic symmetries. In short, the approach has the potential to help explain why time began, and why it might end. As Arkani-Hamed put it, “The thing that we’re bootstrapping is time itself.” 
 
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14 Nov 2020 11:15

A-L-E-X wrote:
Source of the post One curious pattern cosmologists have known about for decades is that space is filled with correlated pairs of objects: pairs of hot spots seen in telescopes’ maps of the early universe; pairs of galaxies or of galaxy clusters or superclusters in the universe today; pairs found at all distances apart. You can see these “two-point correlations” by moving a ruler all over a map of the sky. When there’s an object at one end, cosmologists find that this ups the chance that an object also lies at the other end.

The simplest explanation for the correlations traces them to pairs of quantum particles that fluctuated into existence as space exponentially expanded at the start of the Big Bang.

... huh?  :?

Okay, the method they are referring to is the two-point correlation function, which is a standard technique in cosmology. But correlations are not 'unexpected' or 'curious', nor does their cause have anything to do with what they are claiming. We would expect no correlation if galaxies on all scales were randomly distributed, but they aren't. They are clustered, so we get more correlation on smaller scales, as you can see in this plot:

Image
Source: The clustering of galaxies in the SDSS-III Baryon Oscillation Spectroscopic Survey. Here the correlation function ξ is the vertical axis, and the horizontal axis is the distance in Mpc (but scaled by h, where h=0.7 if the Hubble constant is 70km/s/Mpc). 

As expected there is higher correlation on small scales, due to clustering, and there is also a peak in the correlation function at around 107Mpc/h (or about 150Mpc if h=0.7), which corresponds to the Baryon Acoustic Oscillation. Again, no weird quantum physics there, this is instead a consequence of 'primordial sound waves' in the young universe, which also show up in the cosmic microwave background when we measure its angular power spectrum.

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