Two events may be simultaneous for some but not for others

Superfact 5 : Two events may be simultaneous for some but not for others

Two events may be simultaneous for some but not for others. This means that two events that are simultaneous to an observer may happen at different times to other observers. If two lamps A and B turn on at the same time according to observer #1, lamp A may turn on first for observer #2, and lamp B may turn on first for observer #3. All three observers are correct because time is relative.

Previous Fact:

My previous blog post “The Speed of Light In Vacuum Is a Universal Constant” explained that the speed of light in vacuum compared to yourself is the same regardless of your motion or the origin of the light beam. A beam from a flashlight you are holding is traveling at a specific speed c = 299,792,458 meters per second as compared to you. If your friend is traveling at half the speed of light compared to you, he will still agree that the light beam from your flashlight is traveling at the specific speed c = 299,792,458 meters per second as compared to him, just like his own light beam by the way.

No matter how everyone is traveling everyone agrees that all light beams everywhere, emanating from everyone’s flashlights, all travel at exactly the same speed c = 299,792,458 meters per second. Like I said, the speed of light in vacuum is a universal constant. This is made possible by accepting that space and time are relative, but what does that mean? As mentioned in the other post this leads to the special theory of relativity.

I can add that since we are talking about relativity, or rather special relativity, relativistic effects have been very well tested by thousands of experiments and are not in doubt by the scientific community. Don’t be fooled by the word “theory” in special theory of relativity. “Theory” is not used the same way in science as in everyday language.

Two people Alan and Amy. Alan is on the ground. Amy is flying by Alan in a rocket speeding left. Both Alan and Amy are pointing lasers to the left.
In this picture Amy is traveling past Alan in a rocket. Both have a laser. Both measure the speed of both laser beams to be c = 299,792,458 meters per second.

Relativity of simultaneity

Time is relative not only means that clocks are running slower in moving systems or that distances are contracted. It means that observers will disagree on how fast clocks are running and even disagree on whether events are simultaneous or not and in which order events occur.

If you are traveling through space at a very high speed and your wife/husband is back on earth, you can’t really ask yourself, “I wonder what my wife/husband is doing now?”, because what time it is back on earth depends on how it is calculated and by which observer. There is no universal now. Time is not absolute. Time is relative. The speed of light in vacuum is what is absolute.

I should add that if you combine space and time into spacetime you get an entity that is the same for all observers, the spacetime interval. You can say that in four dimensions the relativity disappears, but that is beyond the scope of this blog post.

Three pairs of lamps and three people. The setup is used to show three situations | Two events may be simultaneous for some but not for others
Amy is traveling at a high speed to the left compared to two lamps A and B. Alan is standing still compared to the lamps. Adam is traveling at a high speed to the right compared to two lamps A and B. Alan turns on the lamps at the same time. After considering the travel time of the light she sees, Amy concludes that lamp B turned on first. After considering the travel time of the light he sees, Adam concludes that lamp A turned on first. I should add this non-simultaneity can only happen if the lamps are separated by a distance.

Below I am going to explain what is going on in more detail. If you don’t want to get into the details you can stop reading here. I am not going to explain the theory of special relativity, but I will explain some of the background and it gets a little bit complicated. Explaining scientific theories is not the goal of this blog. The goal of this blog is to list scientifically/expert accepted facts that are still disputed amongst the public or are highly surprising facts. Let’s look at time dilation first.

Time dilation

That clocks run at different speeds as a result of the constancy of speed of light in vacuum is pretty much well accepted. This is called time dilation. If Amy is passing Alan at a high speed, Alan will see Amy’s clocks running slower than his. This can be illustrated by the light clocks depicted below. The light clocks consist of light beams that are bouncing up and down between the floor and a mirror in the ceiling. Since light in vacuum is a universal constant, this is a very precise and reliable clock.

However, from Alan’s perspective the light beam in Amy’s system/spaceship must go farther than in Alan’s system (but note, from Amy’s perspective it is the opposite). Since the speed of all light beams in vacuum is a universal constant Amy’s clock is slower from Alan’s perspective.

Two systems, each with a clock consisting of light beams bouncing between mirrors. In this set up Alan is stationary compared to us and therefore his light beam only moves vertically.
Alan and Amy have identical light clocks. We call the time it takes for the light beam to go from the floor to the ceiling (one clock tick) Dt in Amy’s case and Dt’ (reference frame) for Alan. Amy is speeding past Alan towards the left. From Alan’s perspective Amy’s clock is running slower. Using Pythagoras theorem, it is possible to derive the formula for time dilation shown in the lower left corner.

When you realize that speeds and velocities are relative, a difficulty arises, perhaps even an apparent paradox. Let’s assume that you are flying in a rocket in space, and you meet another rocket, and your relative speed is 10 million miles per hour.

Is the other rocket standing still and you are moving at 10 million miles per hour? Is the other rocket moving towards you at 10 million miles per hour and you are one standing still? Or are both moving at the speed of 5 million per hour towards each other? Who gets to decide? Do we decide what is “standing-still” by tying it to a point on the surface of planet Earth, the center of planet Earth, the center of our solar system, or the center of our galaxy, or maybe another galaxy or an ether that no one can find?

The point is velocities are always compared to something and can be assigned arbitrary numbers. That means that if an observer, Amy, is speeding past another observer, Alan, at a high speed, then Alan thinks that Amy’s clock runs slower, but note, speed is relative, so we can reverse the situation. In fact, Amy thinks that it is Alan’s clock that runs slower.

Two systems, each with a clock consisting of light beams bouncing between mirrors. In this set up Amy is stationary compared to us and therefore her light beam only moves vertically.
It is equally correct to say that Amy is standing still and that it is Alan that is moving fast to the right. This time (pun not intended) the clock ticks Dt correspond to Alan’s clock ticks and Amy’s clock ticks are Dt’.

To understand how this works and why this is not a contradiction you need the Lorentz transform. The Lorentz transform is a so-called coordinate transform that incorporates time and space (as variable x), and it determines the specific time and space coordinate for one system based on the time and space coordinate for another and the relative velocity between the two. The Lorentz transform is a way of keeping account of time and space coordinates and using it correctly resolves any apparent paradoxes.

It is a bit more complicated to derive the Lorentz transform, and it is beyond the scope of this blog post. Suffice it to say that it is the vx/c2 term in the equation that both explains how it is possible for both Amy and Alan to consider the other’s clock slower and introduces the non-simultaneity aspect of special relativity. You have to look at both space and time to get the full picture.

Lorents transform formula | Two events may be simultaneous for some but not for others
The Lorentz transform is a so-called coordinate transform that incorporates time and space (as variable x), and it determines the specific time and space coordinate for one system based on the time and space coordinate for another and the relative velocity between the two.

The Twin Paradox

There is one obvious paradox that I need to address. Let’s say that Amy and Alan are of the same age. Then Amy leaves earth and travels at high speeds toward the star Sirius. From Alan’s perspective Amy’s clocks are running slower and from Amy’s perspective Alan’s clocks are running slower.

What will happen if Amy turns around and returns to earth after visiting Sirius and they meet up again? Will Amy be younger than Alan or will Alan be younger than Amy. Will they both be younger than each other? Well, the latter is not possible. You have to keep count of the time and what happens is that during the decelerations/accelerations necessary for Amy to turn around as well as the speed-up/slow-down around earth, Amy will catch up on the time that she lost with Alan.

In other words, her acceleration will make it so Alan’s clocks will run faster. When she comes back and meets up with Alan back on earth, Alan will be much older than her.

Recommended Reading

Below is some recommended reading on the Special Theory of Relativity.

Note after copying all the text from my word document to WordPress I realized that wordpress cannot handle symblic characters. Thus all my delta-t were turned into Dt. I am sorry about that.


To see the other Super Facts click here

The Speed of Light In Vacuum Is a Universal Constant

Superfact 4 : The Speed of Light In Vacuum Is a Universal Constant

The speed of light in vacuum is a universal constant. The speed of light in vacuum is the same for all observers regardless of their speed and the direction in which they are going. It is always c = 299,792,458 meters per second. If you try to catch up to a light beam and try to travel close to the speed of the light beam, you will not be able to catch up. The speed of the light beam will still be c = 299,792,458 meters per second compared to you no matter how fast you go. This is possible because time and space don’t behave like we expect.

Superfacts

This is the fifth post of my super-factful blog and my fourth super-fact. As I mentioned previously, the goal of this blog is to create a long list of facts that are important and known to be true and yet are either disputed by large segments of the public or highly surprising or misunderstood by many.

These facts are not trivia, they are accepted as true by the experts in the relevant fields, the evidence that the fact is true is impressive, and they are important to the way we view the world and to what we believe, and despite being known to be true they are hard pills to swallow for many. They are not scientific theories or complicated insights but facts that can be stated simply. In a paragraph or less. They may need more explanation than you can fit in one paragraph, but they can be stated, with a brief explanation in just one paragraph.

The Fourth Superfact

My fourth super-fact is that the speed of light in vacuum compared to yourself is the same regardless of your motion. A beam from a flashlight you are pointing forward is traveling at a specific speed c = 299,792,458 meters per second forward, no matter what you are comparing to. It is important to understand that speed is relative. If you drive 95 miles per hour on a Texas highway you are driving 95 miles per hour compared to the pavement, but you are traveling more than 2,000 miles per hour compared to the moon.

However, a light beam will be traveling at the speed of c = 299,792,458 meters per second (186,000 miles per second) compared to the pavement and also compared to the moon, the sun, the galaxy, the fastest spaceship possible and another light beam. The speed of light in vacuum is not relative. For light in vacuum there is only one speed compared to everything.

Someone passing you at the speed of 99.99% of the speed of light in vacuum will measure his flashlight beam to have the speed c = 299,792,458 meters per second and he will measure your flashlight beam to have the speed c = 299,792,458 meters per second and so will you. It is as if c + c = c. 1 + 1 = 1 not 2, didn’t you know? This is logically possible because time and space is different for different observers.

This is quite shocking if you haven’t come across it before and there are a lot of people (not professional physicists) who refuse to believe it. So, in my opinion it is a super fact. In summary:

No matter how fast you travel, or in what direction, or where you are, you will measure the speed of light in vacuum compared to yourself to be c = 299,792,458 meters per second or approximately 186,000 miles per second or 671 million miles per hour. That goes for all light beams passing by you regardless of origin.

The picture shows two people Alan and Amy. Alan is on the ground. Amy is flying by Alan in a rocket speeding left. Both Alan and Amy are pointing lasers to the left.
In this picture Amy is traveling past Alan in a rocket. Both have a laser. Both measure the speed of both laser beams to be c = 299,792,458 meters per second.

In the picture above let’s say Amy is flying past Alan at half the speed of light. If you believe Alan when he says that both laser beams are traveling at the speed of c = 186,000 miles per second, then you would expect Amy to measure her laser beam to travel at a speed that is half of that c/2 = 93,000 miles per hour, but she doesn’t. She measures her laser light beam to travel at the speed of c = 186,000 miles per second just like Alan. This seems contradictory.

The solution that the special theory of relativity offers for this paradox is that time and space are relative and Amy and Alan measure time and space differently (more on that in another post).

The Speed of Light In Vacuum Is a Universal Constant
Time is going to be different for me than for you. From shutterstock Illustration ID: 1055076638 by andrey_l

I should add that the realization that the speed of light in vacuum is a constant regardless of the speed or direction of the observer or the light source was a result of many experiments, which began with the Michelson-Morley experiments at Case Western Reserve University, Cleveland, Ohio in the years 1881-1887.

At first scientists thought that there was an ether, which acted as a medium for light. They assumed that earth would be moving through this ether. What they tried to establish was earth’s velocity through the ether, but all measurements resulted in light always having the same speed, in all directions, all the time, in summer and in winter, no matter in which direction earth was going. At first, they tried to explain this by saying that the ether compressed the experimental equipment and distorted clocks exactly so that it seemed like the speed of light in vacuum always came out the same.

Others said that earth was dragging the ether with it, but that explanation turned out not to hold water. With the special theory of relativity in 1905 those speculations were laid to rest. It was the way time and space were constructed and connected.

This is a drawing of the Michelson interferometer used at Case Western Reserve University
The first Michelson-Interferometer from 1881. It was used to measure the speed difference of two light beams (well a split light beam) with a very high accuracy (for the time). The light traveled with the same speed in all directions and no matter what earth’s position and speed was in its orbit around the sun. This picture is taken from Wikipedia and is in the public domain of the United States.
The speed c = 299,792,458 meters per second is a universal speed limit created by time and space

I should point out that there is nothing magical about the speed of light in a vacuum. Light traveling through matter, like glass or water, does not travel at this speed c, but slower. That is why I keep saying the “speed of light in vacuum” instead of “the speed of light”.

It is also not entirely correct to say that the speed of light in vacuum is a universal constant, because it isn’t only about the speed light. It is just that light that travels unimpeded through vacuum reaches the universal speed limit created by time and space, or the space-time continuum (that’s another post). The light is prevented from traveling infinitely fast by this speed limit, and light is not the only thing behaving this way. All massless particles / radiation is prevented from reaching infinite speed by this universal speed limit and they will also travel with exactly the same speed c = 299,792,458 meters per second compared to all observers, just like light in vacuum.

So how is time and space arranged to cause this universal speed limit? Well, that is a surprising super fact post for another day (I will link to it once I have made the post). I can add that the discovery that light in vacuum is a universal constant changed basically everything in physics. We had to change the equations and the physics regarding not just time and space but energy, momentum, mass, force, electromagnetics, space geometry, particle physics, and much more. The energy and mass equivalency is a direct result of this E = mc2.

Examples:

Below are some examples of what this discovery led to. Again, don’t worry about the details or how it works. I might explain these effects in future super fact posts and link to them.

  • Time for travelers moving fast compared to you is running slower.
  • Length intervals for travelers moving fast compared to you are contracted.
  • Simultaneous events may not be simultaneous for another observer.
  • The order of events may be reversed for different observers.
  • If you accelerate to a speed that is 99.999% of the speed of light you still haven’t gotten any closer to the speed of light from your perspective. Light in vacuum will still speed off from you at c = 186,000 miles per second. You think you’ll keep accelerating but that the light keeps accelerating just as much ahead of you. You cannot catch up. What other observers see is you accelerating less and less and never catch up even though you get closer.
  • Forces, the mass of objects, momentum, energy and many other physical quantities will reach infinity as you approach the speed of light in vacuum assuming you are not a massless particle.
  • Mass is energy and vice versa E = mc2
  • Magnetic fields pop out as a relativistic side-effect of moving charges.
The E = mc2 formula | The Speed of Light In Vacuum Is a Universal Constant
Mass is energy and vice versa, a direct result of the way time and space are related. Stock Photo ID: 2163111377 by Aree_S
Can We Travel Faster Than The Speed Of Light?

So, it seems like we cannot travel faster than the speed of light in vacuum. It seems like the universal speed limit is a hard limit, unlike the speed limits on Texas highways. That is maybe true, at least locally where we are.

However, you could get around it, by what is kind of cheating, by stretching and bending space to the extreme by using, for example, enormous amounts of negative energy. That’s happening to our Universe over a scale of tens of billions of lightyears. I should add that a lightyear is the distance light in vacuum travel in one year. Stretching and bending space is not part of the special theory of relativity. That is Einstein’s General Theory of Relativity.


To see the other Super Facts click here

Economic Externalities Are Spoilers of Free Markets

Superfact 3 : Economic Externalities Are Spoilers of Free Markets

Economic externalities are spoilers of free markets. So called externalities result in unfettered free markets being non-optimal and can render the correct government intervention more effective even from a purely economic perspective. This comes as a big surprise to the market fundamentalists who believe that an unfettered free market is always the best approach for the economy.

An economic externality or external cost is an indirect cost or benefit to an uninvolved third party that arises as an effect of economic activities. They are unpriced components of market transactions.

An example is the gasoline you buy. Burning the gasoline causes pollution that harms other people including those who do not own cars, future generations, and it harms the environment including animals. Society incurs a cost from that pollution that you don’t pay for at the pump. The gasoline producers and vendors do not pay for it either. Unless you add a tax or make other adjustments the act of polluting is free of charge, even though there is a real cost associated with it. It is a cost that is invisible to unfettered “free markets”. It is a market failure.

Note I am putting “free markets” in quotes because the free market does not exist all by itself. It exists within a framework of laws, a banking system, and entities such as limited liability corporations, etc.

In the photo factories are spewing pollution | Economic Externalities Are Spoilers of Free Markets
Pollution is an example of a negative externality. Photo by Chris LeBoutillier on Pexels.com

Economic Externalities

The existence of economic externalities is entirely uncontroversial among economists, including laissez-faire (libertarian) economists such as Milton Friedman, Friedrich Hayek, and Ludwig von Mises, even though Ludwig von Mises said that they arise from lack of “clear personal property definition.” In fact, Milton Friedman, Nobel prize winner in economics, and a leading anti-tax champion, stated that pollution met the test for when government should act, but that when it did so, it should use market principles to the greatest extent possible — as with a pollution tax. The unfettered free market is not optimal.

This simplified supply and demand graph shows two different graphs in blue. One for the private/production cost per unit of a goods and a second that also includes the cost of the externality.
This simplified supply and demand graph shows two different graphs in blue. One for the private/production cost per unit of a goods and a second that also includes the cost of the externality.

However, in my experience the existence of economic externalities is unwelcome news to less educated market fundamentalists, including many libertarian leaning politicians. I don’t have a Gallup poll to back this up, but I believe it is correct to say that economic externalities are controversial among a significant portion of the public despite being a universally accepted and a fundamental concept of economic science. Externalities are known to exist and that is not an easy pill to swallow for some.

Woman with a pill | Economic Externalities Are Spoilers of Free Markets
The existence of externalities is sometimes a hard pill to swallow. Photo by Artem Podrez on Pexels.com
This simplified supply and demand graph also shows two different graphs in blue. Again, one for the private/production cost per unit of a goods and a second that also includes the cost of the externality. In this case the cost for production goes down as quantity increases but the cost of the externality goes up per unit perhaps because increasingly damaging production methods are used as the quantity increases.
This simplified supply and demand graph also shows two different graphs in blue. Again, one for the private/production cost per unit of a goods and a second that also includes the cost of the externality. In this case the cost for production goes down as quantity increases but the cost of the externality goes up per unit perhaps because increasingly damaging production methods are used as the quantity increases.

In the simple supply-demand graphs above we see how the price of a product per unit (private cost / or production cost) varies with the increased quantities produced. In the first graph, as the production quantity increases the production cost per unit goes up perhaps because labor and other resources get increasingly rare. In the second graph, as the production quantity increases the production cost per unit goes down perhaps because production becomes more efficient with increased quantities.

In both cases demand goes down with quantity (the red demand curve/line) because fewer people want to buy more of the product as the quantity increases. In both cases the externality adds a cost. In this case the externality cost per unit goes up because increasingly damaging production methods are used as the quantity increases. There are many possible examples of these graphs, but the point is that the externality adds a cost that reduces quantity sold in a free market, assuming the cost of the externality is accounted for.

Economic Externalities In The Real Word

Unfortunately, in the real world, externalities are often not accounted for, and figuring out the real cost of an externality is a thorny issue. However, if we know the cost of the externality and have a way of accounting for it, perhaps via tax or a fee, then we would reach a new equilibrium, a new optimal price for the product that will include the social cost. I can add that in the 1920’s an economist Arthur Pigou argued that a tax, equal to the marginal damage or marginal external cost on negative externalities could be used to reduce their incidence to an efficient level.

Notice this tax is not for redistributing wealth or bringing revenue for the government but to reduce economic harm to society. There are other ways to address the problem, but this type of tax is called a Pigouvian tax.

A picture of dollar bills | How a Pigouvian tax can reduce economic harm to society.
How a Pigouvian tax can reduce economic harm to society. Photo by Pixabay on Pexels.com

Finally, I would like to give a few examples of negative and positive externalities. Negative externalities could be :

  • Pollution
  • Climate Change
  • Depletion of fish due to overfishing
  • Depletion of other resources
  • Overuse of antibiotics
  • Spam email

Some positive externalities are :

  • A beekeeper keeps the bees for their honey, but a side effect or externality is the pollination of surrounding crops by the bees.
  • Education (societal benefits beyond the individual).
  • Research and development.
  • Innovations
  • Scientific discoveries
  • Vaccination
This is a picture of a beehive
When a beekeeper keeps bees for their honey, a side effect is the pollination of surrounding crops by the bees. This is an example of a positive externality. Photo by Pixabay on Pexels.com

To see the other Super Facts click here

Some Things Cannot be Known

Superfact 2 : Some Things Cannot Be Known

Some things cannot be known. There are things in mathematics and about our physical world that we know can never be known. For example, we can’t simultaneously know both the exact speed and the exact position of small particles (Heisenberg uncertainty principle). This is not because of a limitation of our instruments. It is a fundamental property of the Universe. But there are more examples of unattainable knowledge. In mathematics there are true statements that can never be proven.

“This”Some Things Cannot be Known” is the third post on my super-factful blog. As mentioned, the goal of this blog is to create a long list of facts that are important and known to be true, yet either disputed by large segments of the public or highly surprising or misunderstood by many. They are facts that are so unnecessarily controversial or astounding that I refer to them as super-facts.

This post is about a fact that may be highly surprising to many. Science knows a lot. People without a solid education in science are often surprised when they find out about some of the amazing things we actually do know.

For example, just by studying the light from a distant star, we can determine what elements it is composed of. The star may be composed of 71% hydrogen, 27% helium, 1% Lithium, and 1% other elements, and we can know that just from its light. We can also determine its temperature, the distance to the star, how it is moving compared to us, where it will be 2.5 million years from now, roughly its age and longevity, and more. 150 years ago, we could not have dreamed of this capability.

Bright white star with a planet and a moon | Some Things Cannot be Known
We can know so much about a star from its light. Shutter Stock Illustration ID: 566774353 by Nostalgia for Infinity.

However, there are also many things we don’t know, and what may come as a big surprise, we know that there are things we can never know, no matter how advanced science becomes. Infinite experimentation, super intelligence, a quintillion super geniuses, infinite time, we simply cannot acquire some knowledge. The universe itself forbids some knowledge. It also means that the statement “nothing is impossible” is false.

At least my natural reaction to such a claim is, “come on you can’t say that with certainty”, and I expect many others will feel the same. However, the reason some knowledge will never be attainable is that physical laws as well as mathematics and logic forbid some knowledge. Some things are not meant to be known. I will give four examples in the four sections below: the event horizon, the Heisenberg uncertainty principle, beyond the observable Universe, and Gödels incompleteness theorem.

The Event Horizon of a Black Hole

A black hole is a region of spacetime where gravity is so strong that nothing, including light, can escape it. The boundary of no escape is called the event horizon. If you pass the event horizon you cannot come back out no matter how much energy, you expand. Nothing can escape, no matter, no radiation, not light or other electromagnetic radiation, and no information. Nothing at all can escape. The curvature of time and space itself forbids it.

I should add that right at the event horizon, there is so called Hawking radiation, but without complicating things it is not the same thing as escaping a black hole. You can guess from physical laws what might be inside, but you can never observe and report what is inside to planet Earth.

Black hole devouring a planet.
Black Hole Stock Photo ID: 2024419973 by Elena11

I would also like to add some basic information about black holes. Some black holes are formed when large stars die and collapse. These black holes are estimated to have a mass of five to several tens of solar masses. However, there are also super massive black holes that reside in the center of galaxies.

The super massive black hole at the center of our galaxy, the Milky Way, is called Sagittarius A* and is estimated to have a mass of four million times the mass of our sun. The largest known supermassive black hole TON 618 is 66 billion times more massive than our sun. There are an estimated 100 million black holes in our own galaxy, the Milky Way. One interesting fact is that celestial objects can orbit a black hole, just like planets orbit the sun, but as you get too close you will rush, at the speed of light, into the depths of the black hole.

The Heisenberg uncertainty principle

The Heisenberg uncertainty principle states that it’s not possible to know the position and momentum of an object with perfect accuracy at the same time. Another way of saying that is that we cannot know both the position and speed of a particle, such as a photon or electron, with perfect accuracy. The formula is: dX * dP >= h/4pi , or uncertainty in position (dX) times uncertainty in momentum (dP) is larger than half of Planck’s constant.  There is also an energy and time precision limit : dT * dE >= h/4pi.

These equations basically means that there are no perfectly exact measurements or knowledge. Everything is a bit fuzzy. Planck’s constant is very small, so Heisenberg uncertainty principle does not matter for everyday objects, but it matters when sizes are very small (positions, energies, etc.) Note, Heisenberg uncertainty principle is not because of a limitation of our equipment, but a limit set by a law of physics. It is a limitation set by the Universe if you will.

The picture shows the formula for the Heisenberg uncertainty principle
Heisenberg uncertainty principle Shutter Stock Vector ID: 2380436193 by Sasha701

Beyond the observable Universe

The observable universe is a ball-shaped region of the universe consisting of all matter that currently can be observed from Earth or its space-based telescopes. The radius of the observable universe is 46.6 billion light-years. The size of the observable universe is growing. Unfortunately, at those distances, space itself is stretching/expanding faster than the speed of light. Since no signal or information can travel faster than the speed of light we are losing, not gaining, celestial objects from the observable universe.

In the past we’ve lost many galaxies this way. Since the expansion is accelerating, we will keep losing more galaxies beyond the boundary of the universe and some galaxies were always lost (with respect to observation). I can add that the universe may be infinite.

A picture of a galaxy full of stars.
A view of a galaxy full of stars. Photo by Pixabay on Pexels.com

If we are wrong about the fact that the expansion of the universe is accelerating, then perhaps we can observe more galaxies in the future. But if not, then there are galaxies that we have never observed, galaxies that we can never observe, and there are galaxies that will become unobservable in the future. Depending on the size of the universe we may never be able to observe more than an infinitesimally small portion of the universe. Again, the universe is stopping us from knowing something.

Gödels incompleteness theorem(s)

The theorem states that in any reasonable mathematical system there will always be true statements that cannot be proved. In other words, to find a complete and consistent set of axioms for all mathematics is impossible. There are forever hidden truths in mathematics. For the case of natural numbers this means that there will always be statements about natural numbers that are true, but that are unprovable. I can add that there is also a second incompleteness theorem that states that a formal system cannot prove that the system itself is consistent. Basically, there are limits to mathematics set by logic. And some things cannot be known.

Some Things Cannot be Known
I have a book on Gödels incompleteness theorem, which I have not read, but I will read it before I make a post about it. Photo by Andrea Piacquadio on Pexels.com


To see the other Super Facts click here

We Know That the Earth is Billions of Years Old

Superfact 1 : The Earth Is Billions Of Years Old

The scientific evidence overwhelmingly show that Earth is billions of years old. There is no credible scientific evidence for a young Earth.

This is the second post on my super-factful blog. As I mentioned in my first post the goal of this blog is to create a long list of facts that are important and known to be true yet are either disputed by large segments of the public or highly surprising or misunderstood by many. These facts are not trivia, they are accepted as true by the experts in the relevant fields, the evidence that the fact is true is impressive, and they are important to the way we view the world and to what we believe, and yet they are hard pills to swallow for many. They are not scientific theories or complicated insights but facts that can be stated simply.

In lack of a better term, I am referring to these facts as “super facts” and so far, I’ve made a list of more than a hundred. In addition to just stating the fact I will explain why we know that it is true and discuss the evidence, give background information and provide links. However, my posts will not be deep dives into the topics in question. I will try to remember to suggest resources for further study. I am open to suggestions for super facts as well as challenges to super facts I’ve posted, or other things I written that someone may disagree with. In fact, I would find that helpful, as long as we can discuss the issue in good faith and keep it friendly.

We Know That the Earth is Billions of Years Old
I will certainly be open to counter arguments but let’s keep it friendly. Photo by Ketut Subiyanto on Pexels.com

My first super fact, which is this post,  is “We Know That the Earth is Billions of Years Old”. To some this may seem trivial whilst others dispute it. The scientific community states that Earth is 4.5 billion years old and that humans evolved over millions of years. This is not in dispute among the scientists / experts in the relevant fields, and yet a lot of non-scientists do not believe this. A 2019 Gallup poll showed that 40% of US adults believe that God created humans in their current form within the last 10,000 years. Therefore, I think this is a good example of a super fact.

Photo of Earth from the moon.
Is Earth 4.5 billion years old or 6,000 years old? Photo by Pixabay on Pexels.com. It was originally taken by Bill Anders and published by NASA.

Older Beliefs

As a teenager I believed that Earth was 6,000 years old. That was before I knew much about science. I had read agenda driven books that left out, or wrongfully dismissed the evidence for an old earth while presenting faulty arguments for a young earth. Just learning about the relevant science was enough for me to realize that I had been bamboozled. At first, I dug my heels in, but I eventually realized that the belief that earth was 6,000 years old was not tenable and unsupportable by science.  

If I had known and understood any of what I am posting in this post when I was 14 years old, I don’t think I would have been bamboozled by the young earth creationist books. However, I can add it was not the only time I was bamboozled. I am hoping my blog will lead to some new insights and good reflection including for myself.

A man sitting on a rock by the ocean as the sun sets. He is thinking.
Perhaps some new insight. Perhaps some intellectually honest reflection. Photo by Keegan Houser on Pexels.com

“Old Earth” Vs “Young Earth”

Below I am first presenting some evidence for “old earth” and then some arguments, or faulty evidence, for “young earth”.

Why Earth Cannot Be Less Than 10,000 Years Old

Radiometric dating of meteorite material, terrestrial material and lunar samples demonstrate that earth is 4.5 billion years, or more precisely 4.54 billion years old.

The various measurements include radiometric dating of rocks and crystals and meteorites found in the earth’s crust as well as moon rocks. There are a number of radiometric dating methods, not just carbon-14.

For example, comparisons of the abundance of carbon-12 and carbon-13 has been used to established that the increase of carbon dioxide in the atmosphere comes from burning fossil fuels, not another source of carbon. Radiometric dating methods use the relative abundance of radioactive isotopes in materials. For example, I-129 (Iodine 129) decays to X-129 (Xenon 129) with a half-life of 16 million years. So, if only a quarter of the original amount of I-129 remains you know that corresponds to 32 million years.

There are a lot of other radioactive isotopes with a wide range of half-lives that can be used for radiometric dating, including uranium-lead dating (U-235, U-238, Pb-206, Pb-207), Samarium–neodymium dating, Potassium–argon dating, Rubidium–strontium dating, Uranium–thorium dating, Chlorine-36 dating, Argon–argon dating, Iodine–xenon dating (I-129 – Xe-129), Lanthanum–barium dating, Lead–lead dating, Hafnium–tungsten dating, Oxygen-Oxygen dating (Isotopes O-16, O-17, O-18), Potassium–calcium dating, Rhenium–osmium dating, Uranium–uranium dating, Krypton–krypton dating, Beryllium dating (Be-10 Be-9), and many others as well the mixing of dating methods.

These dating methods use radioactive decay to establish age, and the various isotopes mentioned have half-lives from a few thousand years to billion years.

There are also dating methods that do not use the relative abundance of radioactive isotopes to establish age. In fission track dating you count the “track” markings left in it by the spontaneous fission of , for example, uranium-238 impurities. In this case you don’t need to know the initial abundance of the radioactive isotope.

In luminescence dating methods you don’t even rely on radioactive isotopes but the effect that background radiation has had on materials. Stratigraphy, or stratigraphic dating, is a relative dating method that uses layers of sediment, rock, debris, and other materials to date events.

The image shows a Uranium atom on the left arrows in the middle and an alpha particle, a gamma ray, a proton, a neutron, and an electron on the right.
Radiometric dating uses the rate of radioactive decay and knowledge of initial relative abundances to establish age. Earth comes out to be billions of years old, not 6,000. Stock Vector ID: 2417370135 by grayjay
We can see galaxies that are billions of lightyears away.

This does not establish the age of the earth, but young earth creationists typically also believe in a young universe. In addition, an old universe makes a young earth implausible.

My drawing shows a star on the left, a light ray in the middle, and earth on the right | We Know That the Earth is Billions of Years Old
The light from a powerful stellar object or a galaxy that is five billion light years away took five billion years to reach us.
We know stars are old because they develop according to certain physical processes.

These physical processes give different stars different lifespans. You can establish the age of a star by determining where it is along its development. An example is our sun. It has fused (burned up) up around five billion years’ worth of hydrogen, so we know it is around five billion years old.

The heavier elements in our solar system originate with older stars that burned out and exploded.

Our solar system, the earth and our bodies contain many kinds of elements heavier than iron. However, elements above iron in the periodic table cannot be formed in the normal nuclear fusion processes in stars. But they can be formed when massive stars die in a supernova explosion or when neutron stars (dead stars) collide. A massive star living, dying, exploding in a supernova, and after that the heavy elements are spread all the way to our solar system, is not a process that can take only 6,000 years. It’s millions and billions of years. It is also interesting to note that this means that parts of our body consist of materials originating in faraway dead stars. We are stardust.

Electromagnetic radiation, including light, and heat transfer, travels from the inside of the sun to the surface and this process takes 100,000 years.

The photons are emitted and reabsorbed over and over, which is a relatively slow process inside the side. If the solar system, the earth, the sun, etc., is only 6,000 years old, how can we see the sun?

On the left is my drawing of the sun. On the right is the earth. In the middle are two different arrows, one corresponding to the sun’s internal heat transfer and the other a light ray in vacuum. 100,000 years versus 8 minutes.
Heat / radiation transfer from the inside of the sun to the surface of the sun takes 100,000 years.

Finally, some young earth arguments

Young Creationist Arguments Don't Work

Radioactive decay rates have changed drastically (No!)

First, this is an ad hoc argument that lacks evidence. Secondly this claim cannot work. The rates of radiometric decay (the ones relevant to radiometric dating) are a result of fundamental physical properties of matter, such as the probability per unit time that a certain particle can “tunnel” out of the nucleus of the atom.

You can’t change fundamental physical properties without destroying physics and how atoms work. The claim is also contrary to empirical evidence. For example, analysis of spectra from quasars show that the fine structure constant has not changed over the last ten billion years.

Another problem with this argument is that for a young earth you would need the decay rates to have been millions of times faster in the past, which would require changes in fundamental properties that would have plenty of noticeable effects on processes other than radioactive decay, not to mention the radiation being millions of times stronger than today. That’s a lot of radiation for Adam and Eve to survive. It would have fried everything.

In addition it is also a mystery how the dozens of different radiometric dating methods could have remained consistent with each other throughout time and add the fact that there are dating methods that do not rely on the decay rate of isotopes.

Young earth creationists sometimes make the claim that the initial ratios between isotopes may have been different.

That the initial ratios/condition were different in the past and therefore radiometric dating is unreliable is a better argument, but it also fails. In this case you must take it case by case for each radiometric dating method and situation. There are some rare cases of mistaken assumptions but there are also cases where the amount of the daughter isotope is known to have been zero, which makes it easy and reliable.

The speed of light in vacuum has changed throughout history (No!)

Similar to the situation above, this objection does not work because the light speed in vacuum is a fundamental constant that is not believed to change, and it would be very strange if it could change. It has been measured and no change has been seen. An example is the Einstein’s equivalence of energy and mass E = mc2. If the speed of light once was millions of times faster than now, the energy contained in a kilogram would be a trillion times larger than now. Where did all that energy go?

Another example, from electromagnetic theory the speed of light is determined by the inverse of the square root of the electric constant multiplied by the magnetic constant (see below). You would have to drastically change the strength of the electric and magnetic fields (by the trillions) to get the speed of light to be millions of times faster. If you for example made the electric field a trillion times weaker how would atoms hold together?

Yet another example, Planck’s law features the speed of light in vacuum constant. In physics, Planck’s law describes the spectral density of electromagnetic radiation emitted by a black body in thermal equilibrium at a given temperature T, when there is no net flow of matter or energy between the body and its environment. Changing the speed of light in vacuum would turn light into very slow microwaves. How would Adam and Eve be able to see? Not to mention that the proportionality constant on the right-hand side of Einstein’s field equations has the speed of light in it. Gravity would essentially disappear. The light speed in vacuum shows up in many other physical relations as well.

The equations shown are the speed of light as the inverse of the square root of the of the electric constant multiplied by the magnetic constant, E = mc2, and the equation for the proportionality constant on the right-hand side of Einstein’s field equations.
A few equations in which the speed of light in vacuum is a fundamental constant.

The earth’s magnetic field has been weakening during the last 130 years as if it was formed from currents resulting from earth being a discharging capacitor (claim by Thomas Barnes). This would make an impossibly strong magnetic field already 8,000 years ago.

I remember this being one of the arguments in a young earth creationist book that I read as a teenager. However, there are a number of problems with this claim.

  • The first problem with this argument is that there is no good reason to believe that earth’s magnetic field acts this way. It does not act like a discharging capacitor.
  • We know that earth’s magnetic field has reversed itself several times thus disproving the discharging capacitor model.
  • Thomas Barnes’ extrapolation completely ignores the nondipole component of the field.
Earth is shown with a giant magnet inside | We Know That the Earth is Billions of Years Old
Earth’s magnetic field. Stock Vector ID: 1851166585 by grayjay.

If the earth and the moon were billions of years old there would be a hundred feet thick dust layer from meteorites  on the moon. The moon landing proved otherwise.

This is yet another argument I remember reading in a young earth creationist book (Scientific Creationism by Henry Morris) as a teenager. The problem with this argument, as I would later find out, is that Morris’ claims about a hundred feet thick dust layer was based on faulty and obsolete data. The expected depth of meteoritic dust on the Moon is less than one foot (after billions of years).

An old earth would be covered by 182 feet of meteoric dust.

This is another claim that I remember from Henry Morris’ book. The observed rates used in Morris’s calculations are based on dust collected in atmosphere; this measurement was contaminated by dust from the earth. More recent measurements of cosmic dust influx measured from satellites give an influx rate of about 1% as large, corresponding to a 66 centimeter at most thick over 4.5 billion  years.

Basically, the evidence for an old earth is very compelling whilst young earth objections to that evidence fails, and young earth arguments tend to fail. At least I am not aware of any valid young earth argument. In addition, based on my readings of young earth creationist books, these books tend to be conspiratorial in nature and making implausible claims about scientific community having certain agendas. There is a reason the young earth view is nearly universally rejected by the relevant scientists.

Conclusion

My conclusion is that the fact that we know that the Earth is Billions of Years Old is a super fact. We know it’s true, it is important, and yet large portions of the public reject that fact.


To see the other Super Facts click here