Category: Physics

Time Dilation Goes Both Ways

Super fact 38 : If two observers are moving compared to each other both will observe the other’s time as being slower. In other words, both observers will observe the other’s clocks as ticking slower. Time slowing down is referred to as Time Dilation. And this post is about how time dilation goes both ways.

A lot of people know that if someone moves very fast his clocks will run slower. That’s relativity. If someone speeds through space in a rocket ship, close to the speed of light his time will slow down. When one hour passes on earth only half an hour may pass in the rocket. What comes as a shock to many people is when they find out that the converse is also true. When one hour passes in the rocket only half an hour will pass on earth.

Clearly that looks like a contradiction, but there is an explanation. I consider this a super fact because it is so strange and almost impossible for people to believe, and yet it is true.

The image shows two clocks side by side. On the left is a wall clock and on the right a wristwatch | Time Dilation Goes Both Ways
The guy on earth says my clock (left) is ticking double as fast as the rocket man’s clock (right). The rocket man say’s my clock (right) is ticking double as fast as the clock on earth (left). Who is right? Surprisingly both of them.

Postulates of Special Relativity

The two postulates of special relativity are:

  • The laws of physics are the same in all inertial frames of reference. An inertial frame is a system that moves at a constant velocity.
  • The speed of light in a vacuum is constant for all observers, regardless of the motion of the light source.

The first postulate is called the principle of relativity and goes all the way back to Galileo Galilei. It means that no experiment can determine whether you are at rest or moving at a constant velocity. The reciprocity of time dilation follows from this postulate. If the time for the rocket man in the example above was ticking at half the speed compared to the time for the guy on earth and they both agreed, then you could tell who was standing still and who was moving from that fact.

The first postulate demands that they disagree. The guy on earth thinks the rocket man’s clock is ticking at half the speed of his own clock, whilst the rocket man think it is earth man’s clock that is going slow. Therefore, you can’t tell who is standing still, which is what the first postulate requires.

The second postulate is the more shocking one and is special to relativity. It was discovered experimentally at the end of the 19th century but was too difficult for scientists to accept at first so various ad hoc explanations were put forth to explain it away, until the theories of relativity were created. I designated this postulate as my super fact #4 and you can read about it here.

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 | Time Dilation Goes Both Ways
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. The speed of light is a universal constant.

Time Dilation

In the pictures below I am showing two rocket systems in space, Amy’s rocket and Alan’s rocket. They are travelling at a high speed compared to each other. Each rocket has a light clock that consists of a light beam bouncing up and down between a mirror in the ceiling and a mirror on the floor. The two light clocks are identical, and each bounce corresponds to a microsecond.

Amy is passing Alan at a high speed, and therefore Alan will see Amy’s light clock running slower than his because Amy’s light beam must travel further. Remember, the speed of light is identical for both light clocks (light speed is a universal constant). For those interested I am also deriving the formula for time dilation.

The picture shows 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.

Since Amy moving left is the same as Amy standing still and Alan moving right you can say that Alan is the one moving fast. In this case it is Alan’s light clock that is ticking slower because from this viewpoint it is his light beam that has to travel further. From Amy’s perspective it is Alan’s clock that is going slower.

The picture shows 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 | Time Dilation Goes Both Ways
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) it is Alan’s clock that is ticking slower. Dt corresponds to Alan’s clock ticks and Amy’s clock ticks are Dt’.

This seemingly contradictory situation is resolved by the fact that Amy’s and Alan’s perspectives will drift apart as they continue their journey. They will increasingly disagree on whether events are simultaneous or not, and they will disagree in which order events occur. This is another shocking fact, or as I refer to it, super fact. It is strange but it resolves the apparent contradiction of reciprocal time dilation. I am explaining this in greater detail in this post.

The Twin Paradox

But what happens if one of Amy or Alan decides to turn around so that they meet up again. If Amy’s clock runs slower from Alan’s perspective and Alan’s clock runs slower from Amy’s perspective, how can you reconcile that when they meet up again? It turns out that whoever is turning around or accelerating or decelerating to turn back is the one who will have the least time pass. If Amy is the one turning back, then she will age less than Alan. During her acceleration she will see Alan’s clock starting to run faster and faster until he is older her.

Let say Alan’s clock is running half the speed of Amy’s clock from Amy’s perspective and Amy’s clock is running half the speed of Alan’s clock from Alan’s perspective. Let’s also say that Amy traveled to the left for 10 years before turning around.

From Alan’s perspective she would have traveled 20 years before turning around. However, from Amy’s perspective 5 years would have passed on Alan’s clock. As she turns around Alan’s clock will run faster and catch up so that when they meet up again Amy will be aged 20 years, while Alan will be aged 40 years. That is 35 years of catching up for Alan’s clock from Amy’s perspective. Alan’s clock advanced 35 years from Amy’s perspective after Amy turned around. In the end Amy will be the younger one.

The picture shows Amy on the left turning around and Alan on the right. Text explains what happens | Time Dilation Goes Both Ways
Observe that the fast-forward advancement of Alan’s clock from Amy’s perspective happens only while Amy is in the process of turning around (accelerating / decelerating). Further, how fast the fast forward happens depends on the distance as well. Once Amy is traveling at a constant speed again (inertial frame) Alan’s clock will run slower again from Amy’s perspective.

A somewhat halting but OK analogy for the 35 years of catching up that happens on Alan’s clock from Amy’s perspective is when you turn a boat around on a wavy sea. As you are moving in the direction of the waves the waves will hit you much less often (if at all) but after you turn around and move against them the waves will hit your boat very frequently. Alan’s clock will run faster for Amy whilst she is turning around.

Book Recommendations on Relativity

To see the other Super Facts click here

Every Symmetry is Associated with a Conservation Law

Super fact 36: Every continuous symmetry of the action of a physical system with conservative forces has a corresponding conservation law. This revolutionary insight was mathematically proven in 1915 by a relatively unknown woman, Emily Noether.

It is not easy to understand what this super fact means, and therefore it is easy to miss the fact it says something fundamental about the nature of reality. It says something profound about our Universe and all possible Universes. It is arguably one of the most profound discoveries in science. Since the discovery of Noether theorem, we do physics differently and we view our physical reality differently.

In the book “The Theory of Almost Everything” the author, theoretical physicist Robert Oerter states that the standard model of elementary particles, or most of modern physics, rests on three pillars, special relativity, quantum physics, and Noether’s theorem. Which one of those three have you not heard of? I guess Noether’s theorem.

That question brings me to the second part of the super fact. Emily Noether did a lot for mathematics and physics in addition to her first theorem (stated above), and yet she is not well known. Albert Einstein said of Emily Noether : “Fräulein Noether was the most significant creative mathematical genius thus far produced since the higher education of women began”. Notice he didn’t say “woman genius”.

Why I consider Noether’s (first) theorem a super fact is because it tells us something fundamental about reality that is highly surprising and yet undisputable (mathematically proven) and not many of us know about it. The second part of the super fact, that despite being one of the greatest geniuses of the 20th century she is so unknown, is also surprising.

A young woman in Victorian clothing sitting at a small table.
This picture reminded me of Emily Noether a genius and one of the greatest mathematicians in human history. This is a submission for Kevin’s No Theme Thursday.

Noether’s Theorem What Does It Mean

Noether’s theorem, says that symmetries in the universe give rise to mathematical conservation laws. One way to understand this is by using an example. That the physical laws remain the same as you translate a system in time is an example of a continuous symmetry.

If you do an experiment twice at two different times, let’s say at 8:00AM and at 9:00AM, and everything is set perfectly identical both times you are likely to get the same result. Well barring statistical/quantum uncertainty. The point is that the physical laws did not change. If the physical laws do not change between 8:00AM and 9:00AM, then you have a continuous symmetry.

Noether’s theorem says that if you have a continuous symmetry, you also have a conservation law, and the conservation law in this case is the conservation of energy/mass. If the physical laws do not change between 8:00AM and 9:00AM then mathematically the total energy / mass of the closed system must remain constant.

It follows that energy is not destroyed or increased. At first it seems like the time symmetry and energy/mass conservation have nothing to do with each other, but the symmetry gives rise to the conservation law. So, if you ask the question, why is energy / mass conserved, the answer is because physical laws don’t change with time.

There are many symmetry-conservation law pairs in nature. Translational symmetry, the fact that the laws of physics stay the same if you move to the side or forward, results in the conservation of momentum. The symmetry of laws that does not change if moving around in a circle amount to the law of conservation of angular momentum. Other symmetries result in the conservation of charge.

The converse is also true. If you find that a quantity is conserved you can find a symmetry, and if you find a symmetry that is broken you can find a quantity that is not conserved after all. There is not much in science that is more fundamental than that and in addition Noether’s theorem is very useful.

The picture illustrates the collision of two balls. It features mathematics demonstrating that linear momentum (mass times velocity) is preserved | Every Symmetry is Associated with a Conservation Law
If the physical laws stay the same when translated in space then linear momentum is conserved. Conservation of momentum principle in isolated system Asset id: 2319593529 by MZinchenko.

Emily Noether

Emily Noether was born into a Jewish family in Germany March 23 in 1882. She was the daughter of the mathematician Max Noether. She studied mathematics and completed her doctorate in 1907. At the time, women were largely excluded from academic positions, but she worked at the Mathematical Institute of Erlangen without pay for seven years. She eventually gained paid positions. She made huge contributions to abstract algebra, calculus of variations, topology and other mathematical fields.

Her most important contributions are the Noether’s theorems, the first one described here. When Hitler came to power in 1933, she had to flee Germany. She got a position as a professor at Bryn Mawr in 1933. She died in 1935.

Black and white photo of Emily Noether wearing a white shirt, a darker skirt and a black bowtie.
Emily Noether in 1910. Unknown author Unknown author Publisher: Mathematical Association of America [3], Brooklyn Museum [4], Agnes Scott College [5], [6], Public domain, via Wikimedia Commons.

Concluding Summary

Noether’s Theorem changes how we view the Universe and the laws of physics. For example, the conservation of energy is not just something we empirically discovered. It follows mathematically from physical laws not changing by time. It represents a paradigm shift in science that arguably is as important as quantum mechanics or relativity and yet very few people have heard of it. I find that quite shocking.

To see the other Super Facts click here

Radon Represents our Largest Exposure to Ionizing Radiation

Superfact 6 : Radon Represents our Largest Exposure to Ionizing Radiation

Radon represents our largest exposure to ionizing radiation. It is responsible for the majority of public exposure to harmful radiation. It is not the sun, the sky, nuclear weapons or nuclear power, or medical treatment, other terrestrial sources, it’s radon. Since we don’t talk much about the very deadly radiation emitted by the radon in our basements that may come as a surprise.

If a radioactive isotope has a long half-life, is that bad? I mean it will be around for a long time. Well, it is complicated. It is important to understand that if the decay rate for an isotope is very slow, in other words, it has a long half-life then it will be less radioactive. If the half-life is 1,000,000 shorter for an isotope X compared to an isotope Y (with a slower decay rate) than it is 1,000,000 more radioactive than isotope Y assuming their decay is of the same type. Short half life means more radioactivity. Long half-life means less radioactivity. The negative aspect of an isotope with a long half-life is that it will be around long, but the positive aspect is that it is less radioactive.

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 | Radon Represents our Largest Exposure to Ionizing Radiation
Radioactive decay is the emission of energy in the form of ionizing radiation. There are different types of decay and the decay-rate for different isotopes vary a lot. Stock Vector ID: 2417370135 by grayjay.

I should explain that isotopes mean that an atom can have a different number of neutrons. For example, carbon (coal) has a few common isotopes. C-12 has 6 protons and 6 neutrons,  C-13 has 6 protons and 7 neutrons,  C-14 has 6 protons and 8 neutrons. The isotope we are talking about when we talk about Radon is Radon-222. That is a really bad one. Radon-222 has a half life of 3.8 days which is 432 billion times shorter than Uranium-238, which has a half life of 4.5 billion years. So, if Radon-222 and  Uranium-238 had the same type of decay (they don’t) Radon-222 would be 432 billion times more radioactive than Uranium-238.

Admittedly Uranium-238 isn’t very radioactive, you can safely hold it, but let’s take Plutonium-238, a famously radioactive isotope with a half-life of 87.7 years. Radon-222 has a half-life that is 8,424 times shorter yielding a decay rate and radiation intensity 8,424 times larger than Plutonium-238.

Radon

An illustration with a blue nucleus surrounded by 86 blue electrons
Radon-222 isotope has 86 electrons, 86 protons and 136 neutrons. Stock Vector ID: 1919418095 by saran insawat

So, Radon-222 is indeed extremely radioactive. But that means it should disappear quickly. Unfortunately, the inside of the earth is constantly supplying more Radon-222 from the radioactive decay and fission occurring there. Nuclear fission (nuclear reactions)  is happening inside the earth providing about half of earth’s heat and powering the movement of Earth’s continents and crust. Since Radon-222 is extremely radioactive and is being resupplied by our own planet it is a very big source of the radiation we are exposed to.

Among all the different kinds of sources it is the biggest one. Since Radon-222 is a natural phenomenon, and we focus on so many other types of other natural and unnatural radiation sources we tend to underestimate the problem. At least I did when we bought our first house. I was asking Radon, what Radon? I think it is a surprising and important fact and therefore a super fact.

Radon Exposure

The various pathways of radon entering a house are shown as red arrows. The house is an illustration.
Illustration of how radon-222 enters a house. Stock Vector ID: 2128365599 by VectorMine.

The WHO estimates that radon exposure alone was estimated to have caused 84,000 deaths by lung cancer in one year. In 50 years, this would be 4.2 million deaths. The WHO predicted that the eventual total death toll from cancer related deaths from the worst nuclear disaster in history, Chernobyl, was 9,000, which is a lot less than 4.2 million. The numbers given by Greenpeace (which WHO does not accept) are up to a million and the Union of Concerned Scientists estimated 27,000.

Those numbers are all still smaller than the estimated deaths from Radon. Keep in mind that the Chernobyl reactor was a very dangerous reactor (RBMK) that lacked a containment shield, a reactor that could never be built in a western country. I can add that according to WHO the predicted future cancer deaths due to accumulated radiation exposures in the population living near Fukushima was between zero and a 100.

According to the United Nations Scientific Committee on the Effects of Atomic Radiation, more than 40% of the average annual human exposure to ionizing radiation is radon in the air. The other sources (all smaller) are cosmic background radiation, terrestrial radiation from the ground, radiation in food and water, exposure to radiation by medical treatment/exams, nuclear testing, Chernobyl, etc. According to former U.S. Surgeon General Richard H. Carmona, Radon is responsible for the majority of public exposure to ionizing radiation. Radon in our basements is indeed a very big deal compared to other radiation sources.

To see the other Super Facts click here

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.

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