# Exploring Lorentz Transformations & Time Dilation Experiments

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• P J Strydom
In summary, Someone learned about Special Relativity and decided to learn about Time dilation. They were told that they needed to learn about the mathematical equation to understand it, but they did not understand it. They then asked for help on a forum and were helped. They then decided to do an experiment to see if what they were told was true. They aimed a laser at a mirror and found that the reflected spot would move even when the Earth was moving.
P J Strydom
TL;DR Summary
Is it possible to test to see if light misses a target when the inferometer moves?
I am totally new to the theory of Special Relativity, but find it very facinating. As a young man I saw a few documentaries on how Einstein saw a clock's movement reaching noon, and how he, traveling in a tram heard the gong only later. He then thought about what if he traveled at the speed of light.

This is just nice things to think about.
I now, after 30 years or so, decided that I would love to understand Special Relativity. As I spoke to people about the theory, I learned that I do not understand how someone traveling very fast, measurable by a fraction of c, would undergo Time dilation. Forget about length contraction, that is even worse for me to understand how a train traveling at say .95% of c will be able to fit in a double garage.
Then some patient people went into depth on what will happen if say one is able to travel just below c towards the moon, that I moved closer to Earth to 300 000 km and not the standard 365k.
I even said I will have a clock on Earth, one on the moon and one in the space ship.

I was assured that if I reach the Moon, my clock on the ship will be slower than the one on the moon.
One guy told me that if this is possible, everyone comparing these two clocks will have one of 2 reactions.
1. They will shake their heads and will not understand it,
2. They will know it was Time dilation and will be able to correlate the difference with Lorentz' transformation.

The more I asked to explain the reasons, the more he told me to learn the Mathematical equation then I will understand it.
To my horror I realized that my algebra was very bad, and I set out to get the transformation equation under my belt.
I also realized that I did not understand what the reasons behind the maths was.
A few great gents on this forum did assist me with a lot I did not know.
Well, I am still not a master of SR, but I do understand where it comes from.

Now, this is one thing I picked up that made my mind ring.
The Michelson Morley inferometer.
The inferometer shows that if a light beam travels in a straight path, through a splitter beam, and gets reflected back to the splitter beam and arrives in a telescope eye piece, it will show that a light beam that traveled perpendicular from this beam, thereby taking a longer path, will also arrive at the exact same time.

Even when they turned this inferometer, and waited 6 months longer and turned it any which way, the inferometer showed the light beam still did not arrive at different times.

I then remember how many "thought experiments" animators made on You Tube, where a train with a "Light clock" traveling at a great speed, say 50% of c, will experience Time dilation, and the light beam will reach the ceiling and floor at exactly the same moment as the beam of a stationary clock.
After I was helped in this forum, I thought, but there is a way to see if this is true.

Now I wonder, has anyone ever done this experiment?
Take a high mountain peak and shine a laser to anothe peak where there is reflecting mirrors concentrating and sending the beam back and forth a few times just to get a lot of distance. (but still short enough to visually see the endpoint on a target board.

What will this light beam show on the target board when Earth's movement is disrupted by the Moon attraction during its different phases?
What will the beam show during the full elipse of the Earth around the sun during all the seasons where the Earth's speed varies?
It is true that the Earth is a moving entity in space, but will it mean the light beam will remain on the bulls eye?
Or will it drift?

Please let me know if such experiments was done.
Greetings

Oh, the beam must be positioned North to south, or South to north.

I'm not quite sure what you are asking. You seem to be reflecting a laser off a mirror and asking if the reflected spot would ever move, neglecting terrestrial sources like earthquakes and air turbulence. If so, then yes, the laser's path is in principle disturbed due to the gravitational effect of the moon and sun. It's completely negligible (back-of-the-envelope, 10-15m, less than the size of an atomic nucleus). And it has nothing to do with the motion of the Earth - it's the change of gravitational field as the sources move that would deviate the beam. Furthermore, this has nothing to do with the Lorentz transforms, which don't apply across a region of spacetime large enough for gravity to have a measurable effect.

You are correct.
After my calculations, one will not see it even over 200 Km.
I want to know if there was ever an experiment done to show that if you have two reference points moving relative to each other as if they are stationary, such as 2 positions on earth, and a laser is shot fom one position to the target position, will one see the laser miss the target, or hit the bulls eye?
The movement of the 2 positions will be North to south and vice versa, to have an effect of the Earth's rotation around its axis, as well as with the Earth moving around the Sun.
In other words, the position of the target and gun on Earth Earth at Midnight will move faster through space than at noon, because we have an effect of the Earth retarding on certain positions such as we have a position on a tyre turning on a road.
I remember they called it angular velocity.
The Earth is now the wheel and the sun the axis. The points on the Earth is now not moving in circles, but in different velocities to the Sun

I did a calculation assuming one can cover a distance of 60 Km with a reflecting laser, which I think is possible.
I then took the axis speed of the Earth at Noon, and Midnight, and added and deducted it from the speed the Earth traverses around the sun.
And worked out what distance the light beam will move on the target.
The light beam will travel from gun to target in 0.0002 seconds.
In this time, the target would move 33 meters per second with the Earth and multiply this with the time the laser took, we will get 0.000001833 mm.
Damit!

Is there any other natural phenoma to prove that if a "light clock" would travel from floor to ceiling, the light beam will really hit its target, and the target would not have moved away?
What about the light beam shot towards the moon over 365 000Km?
Do scientists compensate for a light beam traveling to and fro from the Earth to the Moon?
Does this compensational allowance prove that the light beam traveled the same time as if the Moon was stationary and a beam was shot in a "straight line"?

You seem to be looking for an ether frame. Although I don't think your experiment has been done (it's way too sensitive to atmospheric turbulence to be ever practical), a great many much more precise experiments have been done that prove the point. Michelson-Morley, of course, and a collection of precise measurements of radial and transverse Doppler effects are all consistent with no preferred frame for the propagation of light. Without a preferred frame, there's no basis for saying that the laser and target are moving in any absolute sense - so any laser and target that are at rest with respect to each other will always hit while moving inertially, no matter how the system is accelerated between whiles.

Shirbit.
When I calculated he MM experiment intreferance patern percentages over the distance of 21 odd feet, I also realized that it is way too small to have seen any interferance pattern.
Let me tell you what my problem is and perhaps you will see where my thinking goes.

If a "thought experiment" is animated by some scientists to explain the effects of Time dilation,
1. they propose a Light clock that bounces up and down from a train's floor to its ceiling.
2. Now, I understand it is an exageration, but they will for instance have the clock set at one bounce per second.
3. I then thought, this is exactly the same as the Michelson Morley experiment!
4. I then look at the annimation, and a claim is made that even if this train travels at say .9 of c, it will still take one second for the light beam to return to its original position, even though the light did not travel in a straight line, but it traveled at Pytagoras' theorem a longer distance than the light clock that is stationary to the one observer.

I then wondered if this will be the case in experimental science?
Thats when I thought to ask if there is any natural occurance that can be applied to prove the theory that a light beam will "hit the target" so to say, if the target and source of the light is in movement in space.

I then exagerated the Light clock thought experiment with the following thinking.
If this light pulse ill travel to and fro in one second, this means the distance of the ceiling is half c = 150 000Km away.
I then wondered if this pulse will actually "hit the target, if the target is in motion relative to another exact light clock?

Is the measurement of light travel from distant moons such as Io or others perhaps evidence of such target shooting?

P J Strydom said:
When I calculated he MM experiment intreferance patern percentages over the distance of 21 odd feet, I also realized that it is way too small to have seen any interferance pattern.

Back of the envelope, a velocity dependent fringe shift will be of order ##v/c## (edit: oops, this should be ##v^2/c^2##, so this is all wrong - see posts#12 and #13 below), which works out to be about 1.5×10-6 for Earth's rotation. Multiplying by 7m (your 21 feet) gives us an expected path difference of about 10-5m, which is around 20 wavelengths for light. That's easily detectable with an interferometer - tenths of a wavelength would be tricky.
P J Strydom said:
I then look at the annimation, and a claim is made that even if this train travels at say .9 of c, it will still take one second for the light beam to return to its original position, even though the light did not travel in a straight line, but it traveled at Pytagoras' theorem a longer distance than the light clock that is stationary to the one observer.
You are misunderstanding the experiment. In the frame where the train is at rest, it will take 1s for the light to bounce up and back. It cannot do otherwise if the principle of relativity is true. In the frame where the train is moving at 0.9c then sure it takes more than a second. That's time dilation.
P J Strydom said:
I then wondered if this will be the case in experimental science?
Yes. See the "experimental basis for special relativity" FAQ pinned at the top of this forum.
P J Strydom said:
Is the measurement of light travel from distant moons such as Io or others perhaps evidence of such target shooting?
We've made plenty of measurements of astronomical objects. All are consistent with relativity, and inconsistent with a preferred frame for light. Again, see the thread at the top of the forum.

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P J Strydom said:
...I do not understand how someone traveling very fast, measurable by a fraction of c, would undergo Time dilation.
Time dilation occurs even at slow speed. If the speed is not a significant fraction of c then time dilation is too small (in most cases) to affect anything.

Secondly, time dilation is not something that someone undergoes. To the person it's happening to nothing is amiss. Only the person who is moving at a different speed is able to measure it.

Ibix said:

Back of the envelope, a velocity dependent fringe shift will be of order ##v/c##, which works out to be about 1.5×10-6 for Earth's rotation. Multiplying by 7m (your 21 feet) gives us an expected path difference of about 10-5m, which is around 20 wavelengths for light. That's easily detectable with an interferometer - tenths of a wavelength would be tricky.

You are misunderstanding the experiment. In the frame where the train is at rest, it will take 1s for the light to bounce up and back. It cannot do otherwise if the principle of relativity is true. In the frame where the train is moving at 0.9c then sure it takes more than a second. That's time dilation.

Yes. See the "experimental basis for special relativity" FAQ pinned at the top of this forum.

We've made plenty of measurements of astronomical objects. All are consistent with relativity, and inconsistent with a preferred frame for light. Again, see the thread at the top of the forum.
Yes, so true.
But I really made an effort to re calculate the MM inferometer and saw my mistake.
I took the horisontal plane from Splitter beam and reflector back, and the reflector perpendicular to it and took the assumption that:
The Inferometer length is 7 meters, traveling through aether at the equator speed of 460 M/sec.

I came up when calculating that in this circumstance the difference between the 2 beams would have to be about 10.5%

Is this correct?
If so, 10% on the wavelength , seing that when turned 90 degrees, it will give a total difference of just over 20%, and it will show an interferance pattern.
If I calculated the correct answer, then this inferometer is evidence that light travels at c, no matter where one observe it.
But, does this mean that we can travel faster than c, but will not overtake a light beam?

P J Strydom said:
I came up when calculating that in this circumstance the difference between the 2 beams would have to be about 10.5%
What measurement would have to be 10.5% of what measurement, in order to do what?
P J Strydom said:
But, does this mean that we can travel faster than c, but will not overtake a light beam?
No. How could we travel faster than something and not overtake it? That would be self-contradictory.

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Will we evr know if we are already traveling faster than
Ibix said:
What measurement would have to be 10.5% of what measurement, in order to do what?

No. How could be travel faster than something and not overtake it? That would be self-contradictory.
Sorry man.
on the MM inferometer, with the reflector beams 7 meters away from the splitter beams, and we assume an aether wind of 460 Km (equator speed of earth).
The perpendiculat light beam were supposed to travel 10% longer than the beam traveling parallel to the Aether wind.
Now, turning the inferometer 90 degrees will have an opposite measurement, and if the first measurement was 10%, this will show a doubling measurement resulting in 20%.
and Michelson Morley did not see this difference.
I took the measurements, and physically calculated the distance every beam will travel, and got to 9.8553% difference between the 2 beams on the above data.
All I would like to know is if I came to the correct answer. (the difference MM were looking for)

P J Strydom said:
on the MM inferometer, with the reflector beams 7 meters away from the splitter beams, and we assume an aether wind of 460 Km (equator speed of earth).
The perpendiculat light beam were supposed to travel 10% longer than the beam travelling
I rather doubt that. According to Wikipedia the fringe shift depends on ##v^2/c^2## (not ##v/c## as I guessed above), and taking the ratio of the expected longitudinal and transverse path differences gives ##1/\sqrt{1-v^2/c^2}\approx 1+v^2/2c^2##. The Earth's rotation speed is about 460m/s (not km/s, which I guess is what you meant by Km). That makes the fractional length difference approximately 10-12. Your figure is about a hundred billion times larger, so you would seem to have a calculation error.

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P J Strydom
Michelson and Morley, incidentally, were not attempting to detect any effects based in the rotation of the Earth. Rather, they were attempting to detect effects from its orbital motion. At 20,000m/s, or thereabouts, it's about 400 times greater than the equatorial rotation speed.

Ibix said:
I rather doubt that. According to Wikipedia the fringe shift depends on ##v^2/c^2## (not ##v/c## as I guessed above), and taking the ratio of the expected longitudinal and transverse path differences gives ##1/\sqrt{1-v^2/c^2}\approx 1+v^2/2c^2##. The Earth's rotation speed is about 460m/s (not km/s, which I guess is what you meant by Km). That makes the fractional length difference approximately 10-12. Your figure is about a hundred billion times larger, so you would seem to have a calculation error.
When I read what you said, I just laughed at myself.
It is really a case of me attempting to run a marathon with no legs.
I decided now here and then, I will not continue my quest to understand Time dilation.
It will need someone to sit next to me for a month to make sure I know what the hell I am talking about.
Then another month to teach a baby physics.
Therefore I am in great debt to you and the other gentleman who did listen to me.
If ever I do learn what you know, I will visit again.
Greetings.
Oh, I like the forum and will pop into read the articles posted.

## 1. What are Lorentz Transformations and how are they related to time dilation?

Lorentz Transformations are a set of equations that describe how space and time coordinates change between two reference frames that are moving relative to each other at a constant velocity. Time dilation is a phenomenon predicted by these equations, where time appears to pass slower for an observer in a moving reference frame compared to an observer in a stationary reference frame.

## 2. How do scientists conduct experiments to explore Lorentz Transformations and time dilation?

Scientists use a variety of experimental techniques, such as high-speed particle accelerators, atomic clocks, and spacecraft, to study the effects of Lorentz Transformations and time dilation. These experiments involve measuring the behavior of particles or objects moving at high speeds or in different reference frames.

## 3. What evidence supports the validity of Lorentz Transformations and time dilation?

The predictions of Lorentz Transformations and time dilation have been confirmed by numerous experiments, including the famous Michelson-Morley experiment, which showed that the speed of light is constant in all reference frames. Additionally, the effects of time dilation have been observed in high-speed particle collisions and in the behavior of atomic clocks on airplanes and satellites.

## 4. How do Lorentz Transformations and time dilation relate to Einstein's theory of relativity?

Lorentz Transformations and time dilation are key concepts in Einstein's theory of special relativity, which revolutionized our understanding of space and time. Einstein's theory states that the laws of physics are the same for all observers in uniform motion, and Lorentz Transformations and time dilation are the mathematical expressions of this principle.

## 5. Are there any practical applications of Lorentz Transformations and time dilation?

Yes, the principles of Lorentz Transformations and time dilation are crucial for modern technologies such as GPS systems, which rely on the precise measurement of time and the effects of time dilation in order to function accurately. These concepts also have implications for space travel and the development of future technologies that involve high-speed motion.

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