Saturday, 8 November 2014

Things to know about Interstellar (2014) Explained - Part 1


SPOILER ALERT: The purpose of this article is to provide explanations about the real, theoretical scientific concepts presented in the film, Interstellar (2014) so that people can have a greater understanding of this unusually complex film. If you haven't watched the film and you do not wish to know the specific details of the film, please stop reading and come back here later if you're interested to know more.

The following explanations are provided based on my understanding of the film after watching it the first time on November 5, 2014 and what I know about the basics of quantum mechanics and Einstein’s Theory of Relativity. Note that these are highly complex theories with lots of mathematical calculations and formula. I've tried my best to make them as short, simple and concise as possible for easier understanding without the maths.

If there are any mistakes found in this article, please kindly provide any comments below so I can rectify it.


For my review of the film, please visit this link:


Murphy's law

 It's a saying that states: 
Anything that can go wrong will go wrong.  

It originally comes from Murphy's Original Law, which states that: 
If there are two or more ways to do something, and one of those ways can result in a catastrophe, then someone will do it.

However, Murphy's law doesn't mean that something bad will happen. It means that whatever can happen, will happen.

Cryosleep/Hypersleep

The process of freezing and storing the body of a person for preservation to prevent tissue decomposition during long periods of interstellar travel so that at some future time the person can be awakened with minimal effects of aging due to gravitational or relative velocity time dilation. (will be explained later)



Differences between Classical Physics and Quantum Physics

Quantum and classical physics are based on different conceptions of physical reality.

Classical physics – Any theory of physics in which the Universe is assumed to have a single, well-defined history. Objects move on well-defined paths and have definite histories. We can specify their precise position at each moment in time. Since classical physics mainly deals with the macroscopic world of daily life, they are successful enough for everyday purposes. In essence, these are the ideas that existed before the development of quantum theory.

Law of Thermodynamics, Classical Electromagnetism, non-linear dynamics and Chaos Theory, Einstein’s Theory of Relativity (special and general), Classical Mechanics (Newton’s law of motion and law of universal gravitation, Lagrangian and Hamiltonian mechanics) are all classical physics.

However, it was found out in the 1920s that classical physics could not account for the bizarre behaviour observed on the atomic and subatomic (microscopic) scales of existence. Therefore, quantum theories were developed, which will be discussed later on.

Now, let me first start on explaining what Einstein's Theory of Relativity is about:

Einstein’s Theory of Relativity – General and Special

Before explaining Einstein's theory, it is best to first explain what dimensions are.

Dimensions The number of coordinates required to specify a position or location. These can range from one (a vibrating ‘string’, from String Theory) to three (in space) to 11 (in M-Theory), which will be explained later on.

Space-time – A mathematical space. Its points must be specified by space and time coordinates. It is four dimensional, with three spatial coordinates and one time.

The three macroscopic space dimensions are: (1) left and right; (2) up and down; (3) backward and forward.

Einstein’s Theory of General Relativity 

A theory of gravitation that was developed by Albert Einstein (1907 – 1915). It states that accelerated motion and motion without acceleration but with gravity (standing still in a gravitational field of a given strength) are physically identical (equivalence principle).

Because no special force is required to create inertial effects in an accelerating object, Einstein proposed that we should think the same way about gravity, forgoing the classical notion of gravitational force and instead conceiving of gravity as curves in space-time. This explains phenomena like why light bends in the presence of a gravitational field even though it lacks mass.

According to general relativity, the observed gravitational attraction between masses results from their warping (distortion) of space and time, allowing frame-dragging to occur, whereby a massive rotating object would alter space and time, dragging a nearby object out of position. The shape of space responds to objects in the environment. Therefore, time is a dimension (4) past, present and future; gravity distorts time.

Note: As space contracts, time expands. 

Gravitational waves - Ripples in the curvature of space-time that propagate as a wave, travelling outward from a massive object. Gravitational waves theoretically transport energy as gravitational radiation. (general relativity states that an accelerating mass gives off energy as gravitational radiation.) Gravitational waves cannot exist in the Newtonian theory of gravitation (In Newtonian model, gravity propagates instantaneously - infinite speed. In general relativity, gravity propagates at the speed of light - finite speed.)

Speed of gravity (or speed of a gravitational wave) has not been measured in the laboratory because gravitational interaction is too weak, and such an experiment is beyond current technological capabilities. However, recent discoveries of binary pulsar (a rapidly spinning neutron star that orbits another neutron star or white dwarf) and its observations have shown indirectly that gravitational waves exist.

Einstein's description of gravity:
  • The more massive an object is, the greater the distortion (gravitational influence) it causes in the surrounding space.
  • The distortion becomes weaker (amount of spatial warping decreases) as the distance between objects becomes larger.
Examples:
  • In our solar system, the presence of mass (the sun) causes the fabric of space and time around it to warp (distorted). This distortion causes other surrounding objects (planets) to move around the sun and their motion is determined by the shape of the warp (elliptical orbit).
  • Earth, being a massive object, also warps the fabric of space and time, but far lesser than the sun. This is how the Earth keeps the moon in orbit and each of us bound to its surface.
Earth causes the fabric of space and time to warp, the moon is kept in orbit around the Earth because it rolls along a valley in the warped spatial fabric. In more precise language, it follows a “path of least resistance” in the distorted region around the Earth.

The theory states that time goes more slowly in the presence of a gravity field (Gravitational time dilation) and that the universe is expanding, in some cases faster than the speed of light, because it’s the space itself that’s expanding, not objects within it.

Artificial Gravity

The effects of zero gravity in space is normally the big problem that we, as humans will face with long-term interstellar space travel. We were born on Earth and therefore our bodies are adapted to survive under gravity, but when we’re in space for long periods of time, our muscles will degrade.

To prevent this from happening, scientists have created different designs of installing artificial gravity on spaceships. One such way is to rotate the spacecraft, as shown in the film. The rotation creates a centrifugal force that pushes objects to the outer walls of the spacecraft. This push acts similar to how gravity would, but just in an opposite direction.

You experience this same form of artificial gravity when you’re driving around a tight curve and feel like you’re being pushed outward, away from the central point of the curve. For a spinning spacecraft, your wall becomes the floor on which you walk.

Infographics taken from (right click, open image in new tab to enlarge):

Gravitational Time dilation

In the film, Cooper tells his weeping 10-year-old daughter, Murph, before he flies off to space, “When I get back, we may be the same age.”

To understand time dilation, one must first understand the concept of a reference frame.

reference frame is an imaginary coordinate system that specifies the location and time measurements of events with respect to a fixed origin. It can also be thought of as an imaginary map.

In space-time physics, every person (or observer) has his or her own reference frame in which he/she is the origin. Therefore, a person assigns spatial and time coordinates to events based on his or her position.

Time dilation is the difference between time measurements of two reference frames that are moving at different velocities with respect to one another. Two of the time dilations in Einstein’s Theory of Relativity have been experimentally proven. (the other one is Relative velocity time dilation)

According to Einstein’s Theory of General Relativity, time differs from place to place or time runs more quickly (the actual time speeds up) at higher altitudes because of a weaker gravitational force.

The effect of time passing at different rates in regions of different gravitational potential is called Gravitational time dilation. The lower the gravitational potential (closer to the centre of a massive object), the slower time passes.

Note: The gravitational potential at a location is equal to the work (energy transferred) per unit mass that is done by the force of gravity to move an object to a fixed reference location. As we go closer to the centre of a massive object, the gravity gets stronger, meaning the gravitational potential needed to move an object becomes lesser.

In 2010, gravitational time dilation was measured at the Earth's surface with a height difference of less than 1 meter (12 inches), using optical atomic clocks. The clock at a higher altitude was found to be running faster than the other.

It means that your head ages more quickly than your feet and that people living on the top floor of a tower block age more quickly than those on the ground floor. However, the effect is so small (negligible) that it would add just 90 billionths of a second to a 79-year life span.

In general relativity, the time dilation effect is not reciprocal: an observer at the top of a tower will observe that clocks at ground level tick slower and observers on the ground will agree about that. Gravitational time dilation is agreed upon by all stationary observers, independent of their altitude.

Einstein’s Theory of Special Relativity 

A theory of the structure of space and time developed by Albert Einstein in 1905, which states that:
All the laws of physics are equally valid for all observers in uniform motion (velocity) relative to one another. In other words, the speed of light and the relationship between force (energy), mass, and acceleration are the same for all observers (or reference frames) moving at constant velocity.

The speed of light from a uniformly moving source or in a vacuum is always the same for all observers; regardless of how fast (or slow) the light source or its observer is moving.

The consequences that follow from the special theory of relativity are:

Relativity of simultaneity - simultaneity is not absolute, but dependent on the observer's reference frame. It is impossible to say whether two events occur at the same time if those events are separated in space. So, the perception of Time is relative (dependent on the individual’s or observer’s point of view).
Things that appear to happen at the same time to stationary observer A may appear to happen at different times to moving observer B.

Example: Two plane crashes that happened at the same space. All observers in the same space will agree that both planes arrived at the point of impact at the same time. But where the events are separated in space, such as one plane crash in London and another in Chicago, the question of whether the events are simultaneous is relative: in some reference frames the two accidents may happen at the same time, in others (in a different state of motion relative to the events) the crash in London may occur first, and in others the Chicago crash may occur first.

Length contraction - the physical phenomenon of a decrease in length detected by an observer in objects that travel at any non-zero velocity relative to that observer. This contraction is usually only noticeable when objects are moving near the speed of light; to the direction in which the observed body is travelling.

Example:
At a speed of 13,400,000 m/s, the length is 99.9% of the length at rest; at a speed of 42,300,000 m/s, the length is still 99%.

Mass-energy equivalence

energy and mass are essentially the same thing, and transmutable into each other (neither one appears without the other). Energy always exhibits mass in whatever form the energy takes. The law of conservation of energy is relative to the law of conservation of mass.
The total internal energy, E of a body at rest is equal to the product of its rest mass, m (E = mc2).
Since c2 is a big number, a little mass goes an extremely long way in producing energy.

Relativistic massm = E/c2 for all particles moving at the speed of light. 

Einstein’s formula explains that nothing can travel faster than the speed of light. Nothing outruns electromagnetic radiation – photons (light, radio waves, microwaves, ultraviolet radiation, X-rays, gamma rays, infrared radiation). The faster something moves the more energy it has and from Einstein’s formula we see that the more energy something has the more massive it becomes.
Therefore, a slower-than-light particle with non-zero rest mass needs infinite (or vast amounts of) energy to accelerate to the speed of light; although special relativity does not forbid the existence of particles that travel faster than light at all times (tachyons - hypothetical).

Relative Velocity Time dilation

Time runs at different rates, depending on the relative velocity between two observers (clocks moving near the speed of light operate more slowly than stationary clocks).

However, the only way this can happen is if an observer’s space and time measurements of a system depend on the system’s velocity relative to that observer. This means that two observers can measure the time interval between the same two events and come up with different time measurements for these events, as long as one of the observers is moving at constant velocity with respect to the other. The faster the relative velocity, the slower time passes.

Therefore, when two people synchronize their clocks to read the same time, this synchrony remains as long as the two people remain at rest with respect to one another. However, if one person boards an airplane and flies a certain distance, that person’s clock will run at a slower rate than the person on the ground. This is called Relative velocity time dilation.

When a particle moves horizontally, the total speed of the constituent particles with respect to the rest frame is still equal to the speed of light. The difference, though, is that when the particle is moving horizontally, the total speed of the particle is made up of “orbital speed” and “horizontal speed” components, rather than just an orbital speed component as is the case when the particle is at rest.
The Standard Model of elementary particles shows that every particle consists of smaller particles that orbit each other at the speed of light. That is, each of these particles has an “orbital speed” that equals the speed of light.

Examples:
  • Researchers in the 1970s used atomic clocks to test the theory. One clock remained on the ground, and the other clock flew on a jet at 600 miles per hour. As predicted by Einstein’s Special Theory of Relativity, the clocks ran at different rates. The airplane clock ran billionths of a second slower than the ground clock. (Atomic clocks are known to be so accurate that they lose or gain less than 1 second every 3.7 billion years.
  • In 2010, relative velocity time dilation was observed at speeds of less than 10 meters per second using optical atomic clocks connected by 75 meters of optical fibre.
  • In special relativity, the time dilation effect is reciprocal: as observed from the point of view of either of two clocks which are in motion with respect to each other, it will be the other clock that is time dilated. (This presumes that the relative motion of both parties is uniform; that is, they do not accelerate with respect to one another during the course of the observations.)

It is to note that special and general relativistic effects can combine:

Imagine for any two civilizations with an enormous distance between them (light years apart) and they communicate by transmitting radio waves that travel at the speed of light, the sender will be millennia ahead of the recipient by the time the message reaches the recipient.

Example: 

The satellite clocks are moving at 14,000 km/hr in orbits that circle the Earth twice per day, much faster than clocks on the surface of the Earth, and Einstein's theory of special relativity says that rapidly moving clocks tick more slowly, by about 7 microseconds per day. (relative velocity time dilation)

Also, the orbiting clocks are 20,000 km above the Earth, and experience gravity that is four times weaker than that on the ground. Einstein's general relativity theory says that gravity curves space and time, resulting in a tendency for the orbiting clocks to tick slightly faster, by about 45 microseconds per day. (gravitational time dilation)

The net result is that time on a GPS satellite clock advances faster than a clock on the ground by about 38 microseconds per day. At 38 microseconds per day, the relativistic offset in the rates of the satellite clocks is so large that, if left uncompensated, it would cause navigational errors that accumulate faster than 10 km per day! GPS accounts for relativity by electronically adjusting the rates of the satellite clocks, and by building mathematical corrections into the computer chips which solve for the user's location. Without the proper application of relativity, GPS would fail in its navigational functions within about 2 minutes. (James S. McDonnell)




Sources:





NEXT > PART 2



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