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Einstein’s Theory of Special Relativity SACE38

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Simultaneity - Albert Einstein and the Theory of Relativity

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Hello ppl☺😄

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So, if you had to think about it, the satellite warps its side of the mesh less than the earth, making your device and the satellite's atomic clock experience different gravities and different mesh distortion. This makes the atomic clock run a bit faster. So even if you start the two clocks at the same time, the satellite's atomic clock is going to tick quicker. And that will make your positioning way off if the relativity is not taken into account, in the background calculation of the GPS.

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Well, don't be alarmed. He is not whispering directions to you from his grave. It's just his Theory of Relativity making sure that your GPS is not making you turn a sharp left into a river! You may naturally ask how.

What has a theory from a hundred years ago got to do with how easily your location feature works on your phone?

How do aircrafts manage to make their way and land safely? How is the military able to locate targets? And, of course, something you'll be able to relate to, how is your Uber driver able to track you using the satellite services on a phone?

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The answer is in the way satellites, some 32 of them orbiting around the earth, communicate with your local GPS (or phone) receiver to indicate your precise location. Positioning happens when the satellites talk to your device and a calculation takes place in the background. As long as the precise satellite locations are known, the time it takes the signal to travel at the speed of light gives the distance, and hence, the location of the device. If you made it through middle school math, and physics, this should sound highly doable. If not, we can dedicate a whole other article to long division.

How your GPS works. Image - Pixabay

Is that all it takes to go from your house to the mall?

What makes the technology accurate is however more complicated than simple calculator math. And this is where Einstein's theory of relativity comes in. For about ten years, Einstein successfully worked on the Special and General theory of relativity, culminating his study in 1915. They were essentially maps to understanding motion, physical interactions and the concept of gravity; quite different from Newton's way of thinking.

Newton's 'apple' gravity is simply one of the consequences of the theory at low gravity situations. Nope, this is not a college lecture and you don't run the risk of a boredom attack. Maybe this will come in handy when you want to show off the brains to your next date! Much better than weather chat, trust us.

A teaser for Einstein's General Relativity

So, the general theory of relativity says that we are surrounded by an imaginary web of space and time. This web thing gets warped and stretched when you, say, sit on it. And the extent of the warp is related to how big of a mass is sitting on it. An elephant will pucker the web more than you would. And gravity is then just an expression of how much of a warp it is. Does this sound too sci-fi ish? Well, there's proof.

All interactions, between bodies, then happen over this mesh. Say, if you were to wildly move your arms about in a swimming pool, you would see waves in the water as a result of your actions. Now imagine two massive massive black holes happily warping their part of the space-time mesh. If they were to start rotating about each other (like your flaying arms were), and then collide, there would be distortions in the mesh that would ripple out. That is a gravitational wave!

See, you already know more about Physics than your dad!

Gravitational Waves stretching and compressing space. Light will take less time to travel between Mr.A & Mr.B, as compared to Mr.X & Mr.Y. And that difference is what an interferometer measures. Image - selfdrawn

Having established your geeky street creds, how do you know whether these waves are a real thing? Well, you see the gravitational wave squeezes space, say horizontally, while extending it vertically so that everything, including the earth's space time mesh is distorted too, as it ripples through. The only way you can detect that ripple, while existing in a compressed or expanded mesh yourself would be to measure how long it takes for light to travel between a set of mirrors. If you are along the compression, the time taken would be less, while if you are along the stretched direction, the time would be more. But this is a tiny tiny, very tiny distortion.

The wonder equipment that measures this time difference is an interferometer, known as LIGO. And in 2015, a hundred years after Einstein signed his name on the general theory of relativity, LIGO picked up a signal indicating a space distortion of 10^-19 meters (that's like 0.0000000000000000001 meters). This signal came from two black holes having collided more than a billion years ago! Talk about finding needle in an haystack the size of the universe! This very very important experiment laid bare a further proof of Einstein's theory.

But how did Einstein's theory make your GPS accurate?

Let's move on to your GPS device, now that we have established grounds for caring about space time mesh and that different masses distort the mesh differently. So, if you had to think about it, the satellite warps its side of the mesh less than the earth, making your device and the satellite's atomic clock experience different gravities and different mesh distortion. This makes the atomic clock run a bit faster. So even if you start the two clocks at the same time, the satellite's atomic clock is going to tick quicker. And that will make your positioning way off if the relativity is not taken into account, in the background calculation of the GPS.

For feels, imagine if there was an offset of 0.001 second, your GPS would be off by 300 km.

And that is how Einstein keeps you from landing in the Atlantic!

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Here's How Einstein's Theory of Relativity Is Helping You Take A Left At The Next Signal

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Well, don't be alarmed. He is not whispering directions to you from his grave. It's just his Theory of Relativity making sure that your GPS is not making you turn a sharp left into a river! You may naturally ask how. How do aircrafts manage to make their way and land safely?

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One technology you probably use everyday that wouldn't work if it wasn't for Einstein's theories is GPS, or the global positioning system.

GPS is a network of satellites orbiting Earth. The satellites are constantly emitting signals with their location and the time the signal is emitted. A GPS receiver on Earth uses that information to determine how far it is from different satellites and triangulates that information to find your location. General relativity tells us that gravity affects time, and because the pull of gravity is stronger on Earth than in the satellite's orbit, time is passing faster up where the satellites are than on Earth. GPS technology corrects for this discrepancy, which, unaccounted for, would make the location determined by your GPS receiver inaccurate.

Kip Thorne, Feynman Professor of Theoretical Physics, Emeritus, at Caltech, explains how GPS works, and why it wouldn't if we were ignorant of relativity.
Fusion's original Relatively Speaking series celebrates the 100th anniversary of Albert Einstein's general theory of relativity.

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Why GPS Wouldn't Work Without Einstein's Theory of Relativity

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One technology you probably use everyday that wouldn't work if it wasn't for Einstein's theories is GPS, or the global positioning system. GPS is a network of satellites orbiting Earth. The satellites are constantly emitting signals with their location and the time the signal is emitted.

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Sorry madam hafta upload here cause no padlet for this yet :)

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Ask the average person what "relativity" means, and you'll likely hear answers such as "everything's relative," "you can't go faster than light" or even the classic formula "E = mc ²."

However, if you ask how relativity affects his or her life on a daily basis, you'll probably hear "don't know" or "it just doesn't." These are not surprising answers, but they fall far short of reality.

Here's why. While the tangible effects we ascribe to Einstein's General Theory of Relativity (1915) can be arcane (and range from the fact that clocks in motion run slower to the notion that lightwaves can be bent by gravity), those effects seem far removed from everyday concerns. That is not the situation at all.

For example, consider the Wide Area Augmentation System (WAAS), a navigation system developed for civil aviation that promises exceptional accuracy. The WAAS collects and processes global positioning system (GPS) data, then corrects the initial rough accuracy of 10-20 meters down to about a single meter. It does this by adjusting for atmospheric disturbances and propagation anomalies using ground-based markers at precisely known locations with satellite links to aircraft to report GPS distortions in real time.

Relativity and its consequences figure prominently into GPS. Without the theory that Einstein described almost 100 years ago, critically important navigation tools like GPS and WAAS would not exist.

WAAS improves safety and performance during all phases of flight and especially during the critical landing phase. It does this largely due to the enhanced vertical guidance it provides. However, before any WAAS corrections can be made, the initial GPS readout must achieve a locational accuracy performance in the 1-meter range.

That's a problem because basic GPS would only be accurate to a few miles at best, at least without added receiver compensation to account for the relativistic effects of satellite motion and acceleration, not to mention how these affect the relationship between time and space. While accuracy to a mile might be good enough for rough position reckoning in the air or on open water, it would not be precise enough for WAAS-enhanced runway location and landing guidance (not to mention driving, geolocation and the many others uses we now confidently use based on GPS).

In brief, GPS works this way: each satellite in a constellation of orbiting satellites transmits a unique code data stream. A GPS receiver on Earth picks up these streams and then correlates them with each other. At least four simultaneous signals are needed for a three-dimensional position fix. The timing of the code streams is established by on-board atomic clocks. By analyzing the results of the correlations, the receiver is able to determine the unique position on Earth that resulted in those code sequences at those specific times.

Simple enough, but there's a catch. Unless the errors due to the effects of relativity are considered and the algorithms enhanced to compensate and correct those errors, the locational "answer" the GPS receiver provides will contain an accumulation of errors. In the world of GPS, a few hundredths of a nanosecond difference in time can make an unacceptably large difference between the correct result and the initially computed value. In other words, a commercial airline pilot on an instrument approach to a major airport can't afford to gamble with inaccurate GPS data.

How these relativity errors occur is explained by Prof. Neil Ashby (References 1 through 3, below). He points out the many ways that relativity "corrupts" the intuitive time, distance and motion relationships that we assume in our non-relativistic daily life. Among them:

* Due to the height of the orbit (20,000 km), the GPS satellites are at a lower gravitational potential than clocks are at the Earth's surface; the result is that their atomic clocks run slower and are shifted in frequency.
* Due to their continuous acceleration as they orbit, the satellites' clocks experience time dilation and, again, run slower than on Earth.
* The Earth's rotation relative to a GPS satellite's orbit affects their relative paths and timing relationships.
* The satellites' orbits are not perfect circles; they are elliptical, so the variations are also cyclical. This means that a mere 1% eccentricity in orbit results in a 28 nanosecond timing variation.
* Everything is moving with respect to everything else: Earth-based receivers move with respect to a single satellite and the satellites move with respect to each other. This makes it difficult to establish a frame of reference and remain consistent within it. (Detailed in Reference 4, below.)

Given all these unavoidable error sources, how does a basic GPS receiver provide 1-meter accuracy and even improves on that if two receivers coordinate with each other?

The answer is that GPS receiver vendors incorporate complex algorithms into their correlation/calculation firmware to correct and compensate for the distortions caused by relativity. That's easier said than done, since the errors are small and sometimes elusive (for example, rounding and truncation errors can negate the calculations). The adjustment algorithms, meanwhile, are fairly sophisticated. To add to the challenge, disagreement among physicists and mathematicians exists about the nature and extent of some of the error sources and how to deal with them.

If the average Joe or Jane insists that Einstein's relativity has no impact on their daily life, that's not the case. Nearly 100 years after Einstein published his theory, its ramifications are critical to a satellite-based positioning system and an aircraft-guidance application that even he did not envision.

References:

1. " Relativistic Effects in the Global Positioning System," July 18, 2006.

2. "Relativity in the Global Positioning System," Living Reviews in Relativity, January 2003.

3. "Relativity and the Global Positioning System," Physics Today, May 2002.

4. Richard H. Battin, An Introduction to the Mathematics and Methods of Astrodynamics, ISBN: 978-1-56347-342-5, American Institute of Aeronautics and Astronautics.

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Ask the average person what "relativity" means, and you'll likely hear answers such as "everything's relative," "you can't go faster than light" or even the classic formula "E = mc 2." However, if you ask how relativity affects his or her life on a daily basis, you'll probably hear "don't know" or "it just doesn't."

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Einstein’s Theory of Special Relativity-edited