### Space, time, and spacetime

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This is accomplished by increasing the sensitivity of our detector allowing us to detect these incredibly faint signals. One of the main issues with gravitational wave detectors situated on the surface of the Earth is the noise that comes from the environment, and the noise that is always present in the equipment that we to measure the waves. This noise can drown out all of the faint signals from distant gravitational wave sources that we might possibly detect. In order to see these sources we must reduce the noise from all the environmental factors and equipment we use to produce an incredibly sensitive detector.

Whilst playing the game you have the ability to experiment with the many different variables that the detector relies upon such as; the power of your laser, the vibration isolation equipment, cryogenic cooling, the location of the detector and many others. All these need to be realistically balanced, not only in performance, but by how much they cost as you don't have an infinite source of money!

Starting the game from the main screen you are first asked to enter your name and a name for your detector.

## Gravity Probe B

You are then asked to choose one of four options on where you would like your detector to be located. By clicking on each of the locations City, Desert, Island or Forest you can see the various attributes of that location. The higher the number of stars for the Noise the quieter that location will be, i. The greater the number of budget stars the more money you get to start with.

Now you will enter the Principal Investigator's PI office, from which you control the main part of the game. This is the design phase during which you can tweak parameters of the detector in order to make it more sensitive. The sensitivity is determined by sum of various noise contributions. You can always check all the noise curves in the Noise Model screen; this can be opened up at any point by clicking the green graph icon:. You can adjust the subsystem settings while the Noise Model is open and see how the noise in the noise curves change when you change the detectors parameters. The best sensitivity is reached when the total noise, which is the sum of all other curves, is as low as possible over a wide frequency range.

You can close the Noise Model by clicking on the green noise model icon again. From the PI office you can access the design areas for each of the subsystems for your detector. You access each of the subsystems by clicking on each of the monitors on the PI's desk. The following subsystems are available:. Once you are in one of the subsystems you can get back to the PI's office at any point by clicking the house icon on the menu bar.

While you are changing parameters and try for the best sensitivity you must watch the remaining budget:. The more you enhance your detector, the more complex the machine becomes. This could make the operation of the detector more difficult and can cause occasional data loss. Thus your number of detections will be slightly lower when you design a very complex machine. Once you have setup your subsystem settings you then need to begin your 'Science Run' and see how your detector performs.

You do this by clicking the science run button on the desk in the PI's office. Once the detector is 'locked', in other words when all control systems have been engaged and are working, you will see how far away our detector can measure gravitational waves from. Einstein realized that a person who accelerates downward along with the ball will not be able to detect the effects of gravity on it. An observer can "transform away" gravity at least in the immediate neighborhood simply by moving to this accelerated frame of reference — no matter what kind of object is dropped.

### PBS Space Time

Gravitation is locally equivalent to acceleration. This is the principle of equivalence. To understand how remarkable the equivalence principle really is, imagine how it would be if gravity worked like other forces. If gravity were like electricity, for example, then balls with more charge would be attracted to the earth more strongly, and hence fall down more quickly than balls with less charge. Balls whose charge was of the same sign as the earth's would even "fall" upwards. There would be no way to transform away such effects by moving to the same accelerated frame of reference for all objects.

But gravity is "matter-blind" — it affects all objects the same way. From this fact Einstein leapt to the spectacular inference that gravity does not depend on the properties of matter as electricity, for example, depends on electric charge. Rather the phenomenon of gravity must spring from some property of spacetime.

Einstein eventually identified the property of spacetime which is responsible for gravity as its curvature. Space and time in Einstein's universe are no longer flat as implicitly assumed by Newton but can pushed and pulled, stretched and warped by matter. Gravity feels strongest where spacetime is most curved, and it vanishes where spacetime is flat.

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This is the core of Einstein's theory of general relativity, which is often summed up in words as follows: "matter tells spacetime how to curve, and curved spacetime tells matter how to move". A standard way to illustrate this idea is to place a bowling ball representing a massive object such as the sun onto a stretched rubber sheet representing spacetime.

If a marble is placed onto the rubber sheet, it will roll toward the bowling ball, and may even be put into "orbit" around the bowling ball. This occurs, not because the smaller mass is "attracted" by a force emanating from the larger one, but because it is traveling along a surface which has been deformed by the presence of the larger mass.

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In the same way gravitation in Einstein's theory arises not as a force propagating through spacetime, but rather as a feature of spacetime itself. According to Einstein, your weight on earth is due to the fact that your body is traveling through warped spacetime! While intuitively appealing, however, the rubber-sheet picture has its limitations.

Mostly, these have to do with the fact that it allows us to visualize the spatial aspect of Einstein's theory, but not the temporal one.

To see this, we need only remember that Newtonian gravity must be approximately valid, whatever Einstein says, and Newton tells us that bodies move in straight lines unless acted upon by a force. Why, then, do the orbits of planets around the sun on the rubber sheet appear so far from straight, if there is no attracting force reaching out through spacetime to tug on them?

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- What is a space time continuum?.

The answer is that planetary trajectories are very nearly straight — in spacetime , not space. The worldline of the earth, for example, resembles a stretched-out spiral whose width in space is only one astronomical unit, but whose length in the time direction is measured in lightyears! Another way to appreciate the importance of the "time" in "spacetime" is to apply the equivalence principle and ask whether the fact that we experience a gravitational field on the earth's surface is "equivalent" to stating that the earth's surface is continually accelerating outward.

Obviously not, for we do not observe the earth to grow larger! The trouble is that, in speaking of the earth's surface, we have again lapsed into thinking of acceleration in spatial terms. On earth, where speeds are small compared to the speed of light and the gravitational field is weak, it turns out that nearly all of our weight arises due to the warping of time , rather than space.

What this means in practice is that gravity on earth is "equivalent" to acceleration mostly in the sense that clocks on the surface run more slowly than clocks in outer space. General relativity is based physically on the equivalence principle, but the theory also has a second, more mathematical foundation. Known as the principle of general covariance, it is the requirement that the law of gravitation be the same for all observers — even accelerating ones — regardless of the coordinates in which it is described. It is for this reason that Einstein named his new theory "general", as opposed to "special" relativity — he dropped the earlier restriction to uniformly moving observers.

This proved to be the most difficult challenge that Einstein ever faced.

## Time Travel: Theories, Paradoxes & Possibilities

As he later said, to express physical laws without coordinates is like "describing thoughts without words". Einstein was obliged to master the abstract mathematics of surfaces and their description in terms of tensors, a field pioneered by Carl Friedrich Gauss and generalized to higher dimensions and more abstract spaces by Georg Friedrich Bernard Riemann In this labor he was aided above all by his friend the mathematician Marcel Grossmann Another mathematician named David Hilbert nearly beat him to his final equations. But general relativity is above all Einstein's achievement, and the phrase "Einstein's spacetime" is entirely appropriate.

No theory of comparable significance before or since is more nearly due to the struggle of a single scientist.

## Space-Time - Special and General Relativity - The Physics of the Universe

At the end of Einstein wrote to a friend that he had succeeded at last, and that he was "content but rather worn out". He later described this period as follows: "The years of searching in the dark for a truth that one feels but cannot express, the intense desire and the alternations of confidence and misgiving until one breaks through to clarity and understanding, are known only to those who have themselves experienced them". In , Einstein described Mach's principle as a philosophical pillar of general relativity, along with the physical principle of equivalence and the mathematical pillar of general covariance.

This characterization is now widely regarded as wishful thinking.

Einstein was undoubtedly inspired by Mach's relational views, and he hoped that his new theory of gravitation would "secure the relativization of inertia" by binding spacetime so tightly to matter that one could not exist without the other. In fact, however, the equations of general relativity are perfectly consistent with spacetimes that contain no matter at all.

Flat Minkowski spacetime is a trivial example, but empty spacetime can also be curved, as demonstrated by Willem de Sitter in The bare existence of such solutions in Einstein's theory shows that it cannot be Machian in the strict sense; matter and spacetime remain logically independent.

The term "general relativity" is thus something of a misnomer, as pointed out by Hermann Minkowski and others.