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Physics, Astronomy & Cosmology / Re: How does light move in a vacuum?

« on: 02/12/2020 20:39:48 »

The complexity of the mathematics overwhelmed me especially when I found permittivity being defined in terms of 'c'.

You are correct - today it has become a circular argument.
- In in the past 100 years, all our basic measurements have been redefined based on the theory and observation that the speed of light is constant.

Historical Background
When Maxwell originally developed his equations, he combined several laws that had been developed by Gauss, Faraday and Ampere into a set of differential equations.
- One of the predictions of these equations is that if you disturb the electric or magnetic field, part of that energy will set off through space as a self-propagating wave.
- And the constants in his equations define the speed of this wave, which is c= 1/√(ε₀μ₀)
- This was before Einstein's relativity

An Analogy
This is not so different from the equations for vibration of a string, which you may have studied in senior high school.
- In this case, the velocity of the wave is v= √(T/μ)
- where T is the tension of the string, and μ is the mass per unit length of the string
- And we are familiar with musicians tuning a guitar by changing the tension, and also using thicker strings for lower notes
- Of course, a string is a medium, and a vacuum isn't - but if you substitute a medium....
- For the internet, we all make use of pulses of light traveling through optical fiber, which has a different value of ε than a vacuum, here light travels at about 2/3 of c. (ε = ε₀ε_r)
- see: https://en.wikipedia.org/wiki/String_vibration

50 years after Einstein's Relativity
Einstein's assertion that c is the ultimate unchanging speed limit has been thoroughly tested in many different ways.
- And so, in 1960, the definition of length was changed from a certain platinum bar to a certain number of wavelengths of light.
See: https://en.wikipedia.org/wiki/International_System_of_Units#Evolution_of_the_SI

100 years after Einstein's Relativity
Einstein's assertion that c is the ultimate unchanging speed limit has been tested in far more precision in far more scenarios.
- So now, the definition of length has been changed to the distance light travels in a certain amount of time.
- Time is now measured by the frequency of electromagnetic radiation
- Since speed = distance/time, and both distance and time are now defined in terms of light, c is a fixed and unchangeable value, by definition. (Hence the circular argument mentioned at the start of this post.)
- And finally, the kilogram has recently been changed from a certain lump of platinum to a relationship based on light and Plank's constant.

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Physics, Astronomy & Cosmology / Re: Is the speed of light constant?

« on: 29/05/2020 23:52:05 »

Is there a simpler explanation?

Probably the simplest equation to calculate the speed of light in a vacuum:
c = 1/√(ε₀μ₀)
where:
- c: velocity of light in a vacuum
- ε₀: permittivity of a vacuum
- μ₀: permeability of a vacuum
Look at just the last 2 lines of this section: https://en.wikipedia.org/wiki/Electromagnetic_wave_equation#The_origin_of_the_electromagnetic_wave_equation

This is just as simple as the equation for the speed of a vibration on a string (eg a guitar string):
v = √(T/ρ)
where:
- v: velocity of a wave in the string
- T: tension of the string
- ρ: density of the string
Look at just the last 3 lines of this section: https://en.wikipedia.org/wiki/String_vibration#Derivation


For more information:
https://en.wikipedia.org/wiki/Vacuum_permittivity
https://en.wikipedia.org/wiki/Vacuum_permeability

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Physics, Astronomy & Cosmology / Re: Do electromagnetic waves have a fixed speed?

« on: 23/05/2020 11:42:24 »

Deriving the speed of light from Maxwell's equations is similar to Bell's inequality in that both are universally accepted but I have never seen a simply understood explanation for either.

try www.maxwells-equations.com  The video is excellent and links the weird-looking 3-dimensional vector calculus to actual laboratory experiments with electromagnets and capacitors.

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Physics, Astronomy & Cosmology / Re: How do galaxies keep a stable size?

« on: 23/05/2019 16:40:07 »

Individual galaxies do not expand due to the expansion of space because they are compact enough that the mutual gravitational attraction holds them together. This effect actually extends all the way out to include groups of galaxies.  The individual galaxies of our local group are not receding from each other but orbit each other as a gravitationally bound system.  It the larger groups of galaxies that are moving apart from each other.

The individual stars in a galaxy are in orbit around the their mutual center of gravity.  Orbits are not as fragile as some people tend to think they are.  If you slow down or speed up an object in orbit, it will not necessarily "fall out" or "fly off" of orbit.  Unless you make a large change in its speed, it just settles into a new orbit.   So for example,  if you wanted to make the Moon "fall" into the Earth,  you would have to reduce its orbital speed to less than 1/5 of its present orbital speed, and to make it fly away into space, you would have to increase it by almost 41%.   
Galaxies are made of stars that fall somewhere between.  It's a bit more complicated with galaxies, but the general idea is the same. Stars in the galaxies don't have to maintain a delicate balance to remain in orbit and have a fair amount of "wriggle room". *
This is not to say that galaxies don't evolve over time.  Early in their lifetimes, things are a lot less stable.   You still had material falling in towards the center feeding the black hole their, etc.   And even later, and occasional close encounter will fling a star clear of its parent galaxy.  But the vast majority of stars in a mature galaxy are in that "comfort zone" as far as their orbit goes, and would take quite a bit to knock them completely out of it.

* As an analogy, think of a rocking chair.  If you give it a push, it will rock back and forth, but won't fall over. It takes quite a large shove to make it completely topple over.

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Physics, Astronomy & Cosmology / Re: Which force is stronger...gravitation or dark energy?

« on: 12/06/2018 21:52:56 »

Which is stronger depends on the circumstances.  Dark energy has a uniform density, while gravity depends on the amount of mass and the distance from it.   The more you concentrate mass, the stronger the local gravity.   When it comes to things like stars, galaxies and even clusters of galaxies, the mass density is still enough for gravity to dominate.  At scales larger than this, the overall density is low enough that dark energy dominates.