# How do you prove that the speed of light is absolute

• Gigahurtz
In summary, the conversation discusses the question of proving the speed of light as absolute, as well as the concept of time dilation and its connection to the theory of relativity. It is mentioned that scientific theories cannot be proven, but rather tested through experiments and falsification. Suggestions are also given for experiments to explore in the context of time dilation.

#### Gigahurtz

Im doing my science fair project on time dilation, and I am wondering how to prove that the speed of light is absolute.
Can anyone help me?

One thing that comes to mind is to consider the half-lives of particles. Some particles in the laboratory decay radioactively at a certain rate. But I think I read somewhere that particles of the same kind that strike the Earth from outer space (and are traveling really fast) decay at a slower rate. This is evidence that very very speedy objects age more slowly, which is a consequence of the the speed of light being constant.

I'm not sure you can prove it. It's a postulate.

So, the logic is thus:

Let's suppose the speed of light is constant.
Then ...
Thus etc., etc. etc...
And we arrive at Einstein's theory of relativity.

So, since Einsteins' ToR explains what we see exquisitely well, we think it is very likely right, thus our original postulate is very likely true.

DaveC426913 said:
I'm not sure you can prove it. It's a postulate.
Not even that. It is a postulate that, as far as we can tell (see post #4), is completely consistent with nature.

Purely conjecturally (I am not espousing a crank theory!), suppose someone experimentally finds a very slight frequency-based dependency in the speed of light and others confirm the results. While Einstein's postulate will remain an interesting mathematical postulate, it will be in contradiction with how the universe truly works. Einstein's postulate will be deemed as approximately correct.

One can prove things in mathematics. Science doesn't work that way. After seeing thousands of black crows, and never seeing a crow other than black, you might postulate that all crows are black. Scientists worldwide confirm your hypothesis. This does not prove your hypothesis is correct. It will in fact be provably incorrect the minute someone documents finding an albino crow.

jtbell said:
The speed-of-light postulate has also been tested experimentally, many times. See the FAQ Experimental Basis of Special Relativity, in particular section 3.

Being in 8th grade not all of those will probably be something you will want to look at or understand. Still, there are a few that I would suggest looking at in detail. The first would be the Michelson-Morley experiment. This experiment was an important result against the prevailing ether theory of the propagation of light. The experiment showed that the speed of light is invariant to the frame of motion of the Earth. If there was an ether or some fluid through which light propagated, then the motion with respect to the fluid would affect the speed of propagation.

A more modern example in terms of special relativity that I would suggest is particle physics. Like Cantab stated, there are none decay times and half-life of particles which we can compare against in particle accelerators. In an accelerator, the particles produced will travel at relativistic speeds, allowing us to observe time dilation by comparing how long the particles lasted at high speeds with respect to how long they last at rest. I once had a workbook in high school of bubble chamber photos. Using overlays, you could measure the curvature of a path to find the energy and type of particle. You could measure the length of the path and using the energy try to deduce the lifetime. A fun and surprisingly accurate exercise but I do not know what the name of the text was.

Gigahurtz said:
It is. Welcome to Physics Forums.

Gigahurtz said:
Im doing my science fair project on time dilation, and I am wondering how to prove that the speed of light is absolute.
You don't. What you're talking about is a part of the definition of special relativity, which is a scientific theory. Theories can't be proved. Consider e.g. the theory that keys fall towards the ground when dropped from a human hand. It's a valid theory because it makes testable predictions. To prove this theory, you would have to prove all of its predictions, but no matter how many experiments you perform, the theory is always making a prediction that you haven't proved yet. (Dropping the same key a million times doesn't prove that it will fall the next time, but the theory predicts that it will).

Instead, scientific theories are tested by trying to disprove them. If you have proved that a prediction made by the theory is false, the theory is said to have been "falsified". What you should be looking for are experiments with results that are consistent with the predictions of special relativity, but contradict some of the predictions made by Newtonian mechanics (the best theory we had before special relativity). Those experiments don't prove special relavity, but they prove that SR is a better theory than the alternative.

Thanks everyone,
If you know of anything else I could put in my science fair j(on time dilation), it would be very helpful.

I have heard of the Dopler effect, and how that is used in police radar, the red shift/ blue shift.
Would this have any consequence with this question?

Fredrik "What you should be looking for are experiments with results that are consistent with the predictions of special relativity, but contradict some of the predictions made by Newtonian mechanics"

What are some experiments that you would recommend?

Fredrik said:
You don't. What you're talking about is a part of the definition of special relativity, which is a scientific theory. Theories can't be proved.
There's a definition issue here that I think gives the wrong impression. The word "prove" covers a range of levels of verification and does not automatically imply an absolute. The words "evidence" and "proof" are exactly synonomous with each other and so every time you do a successful experiment, you've done more than just not proven it wrong, you've added to the body of proof - you've increased the level to which you can say the theory is "proven". The word "prove" or "proven" should always come with a qualifier that specifies a standard. Ie, when a jury determines someone's guilt is proven, it isn't an absolute, but is "beyond a reasonable doubt". Though there is no specific similar standard in science, you can judge the relative strength of individual theories as, say, 50% proven, 90% proven, etc., even while knowing there is no such thing as 100% proven...

...in math, however, a theorem is either true or false: 100% proven or 0% proven.

...and in the wiki for theory, they quote the National Acadmy of Sciences, and though they don't use the word "proof", they do say "well established". And that's exactly synonomous with "well proven".

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Gigahurtz said:
What are some experiments that you would recommend?
I don't know much about the experiments myself, but the link that jtbell posted above looks like a good start.

Another thing you might want to include is the following very easy* proof that invariance of the speed of light implies time dilation: Imagine a train moving at speed v with a laser attached to the ceiling, aimed straight down. The laser is switched on, and hits the floor a time t0 later according to a clock on the train, and a time t later according to a clock on the ground. These times can't be the same, because to an observer on the train, the distance the light moved is ct0, and to an observer on the ground, the distance the light moved is ct. The times can't be the same because these distances can't be the same. The observer on the ground will agree that the light moved a distance ct0 straight down, but he will also say that it also moved a distance vt to the side.

This means that you can draw a right triangle such that the lengths of its sides are "the distance the light moved in the train's rest frame", "the distance the light moved in the ground's rest frame" and "the distance that the train moved". If you express those distances in the form "velocity*time" (as I did above), you can use the pythagorean theorem to find the relationship between t and t0.

*) Very easy for those of us who spent years studying physics at the university, but probably not so easy but still doable for an 8th grader.

russ_watters said:
The words "evidence" and "proof" are exactly synonomous with each other
I agree with a lot of what you said, but I don't think many people consider those words exactly synonymous. You mentioned that the courts define "proof" with the words "beyond resonable doubt", but I've heard that law students are taught that "evidence" is anything that changes the probability that a given statement is true. For example, if you have a good reason to think there's a 22% probability that statement X is true, and you find something that gives you a good reason to change that to 24%, that's "evidence" of X (and if what you found changed the probability to 21%, that's evidence against X).

In physics, yes. In mathematics, no. Because we are talking about physics the "proof" or "evidence" is "experimental evidence".

How about verifying Ampere's law? I think that can be done with high school apparatus. Ampere's law can be related to Coulomb's law via Lorentz transformations, which are derived by postulating the Principle of Relativity and the constancy of he speed of light for all inertial frames.

http://physics.weber.edu/schroeder/mrr/MRR.html

## 1. What is the speed of light and why is it important to prove its absoluteness?

The speed of light is a fundamental constant in physics, denoted by the letter 'c'. It is the fastest possible speed at which all matter and information in the universe can travel. Proving its absoluteness is crucial because it serves as a crucial foundation for many theories in physics, including Einstein's theory of relativity.

## 2. How was the speed of light first determined and who discovered it?

The speed of light was first determined by the Danish astronomer Ole Rømer in the 17th century. He observed the eclipses of Jupiter's moons and noticed that the time between each eclipse varied depending on the position of Earth in its orbit. From this, he calculated the speed of light to be approximately 225,000 kilometers per second.

## 3. What experiments have been conducted to prove the absoluteness of the speed of light?

One of the most famous experiments is the Michelson-Morley experiment, conducted in 1887. This experiment aimed to measure any difference in the speed of light when the Earth was moving in different directions. However, the results showed that the speed of light was the same, regardless of the Earth's movement, thus proving its absoluteness.

## 4. Can the speed of light ever be surpassed?

According to the theory of relativity, the speed of light is the ultimate speed limit in the universe and cannot be surpassed. This is because as an object approaches the speed of light, its mass increases, and the energy required to accelerate it further becomes infinite.

## 5. How is the absoluteness of the speed of light related to the concept of space and time?

The absoluteness of the speed of light is closely related to the concept of space and time. According to Einstein's theory of relativity, the speed of light is the same for all observers, regardless of their relative motion. This means that space and time are not absolute, but rather they are relative to the observer's frame of reference.