If you are looking for a few paragraph answer to the question "What is Space-Time?" Dr. Sten Odenwald offers one in The Astronomy Cafe:
"In 1906, soon after Albert Einstein announced his special theory of relativity, his former college teacher in mathematics, Hermann Minkowski, developed a new scheme for thinking about space and time that emphasized its geometric qualities. In his famous quotation delivered at a public lecture on relativity, he announced that,
'The views of space and time which I wish to lay before you have sprung from the soil of experimental physics, and therein lies their strength. They are radical. henceforth, space by itself, and time by itself, are doomed to fade away into mere shadows, and only a kind of union of the two will preserve an independent reality.'
This new reality was that space and time, as physical constructs, have to be combined into a new mathematical/physical entity called 'space-time', because the equations of relativity show that both the space and time coordinates of any event must get mixed together by the mathematics, in order to accurately describe what we see. Because space consists of 3 dimensions, and time is 1-dimensional, space-time must, therefore, be a 4-dimensional object. It is believed to be a 'continuum' because so far as we know, there are no missing points in space or instants in time, and both can be subdivided without any apparent limit in size or duration. So, physicists now routinely consider our world to be embedded in this 4-dimensional Space-Time continuum, and all events, places, moments in history, actions and so on are described in terms of their location in Space-Time.
Space-time does not evolve, it simply exists. When we examine a particular object from the stand point of its space-time representation, every particle is located along its world-line. This is a spaghetti-like line that stretches from the past to the future showing the spatial location of the particle at every instant in time. This world-line exists as a complete object which may be sliced here and there so that you can see where the particle is located in space at a particular instant. Once you determine the complete world line of a particle from the forces acting upon it, you have 'solved' for its complete history. This world-line does not change with time, but simply exists as a timeless object. Similarly, in general relativity, when you solve equations for the shape of space-time, this shape does not change in time, but exists as a complete timeless object. You can slice it here and there to examine what the geometry of space looks like at a particular instant. Examining consecutive slices in time will let you see whether, for example, the universe is expanding or not."
This is the relatively simple, widely accepted, description of SpaceTime. Our links will give you a solid understanding of the SpaceTime theories that most scientists believe are correct. But this definition of SpaceTime only scratches the surface of the incredibly fascinating Alice in Wonderland like world of Physics.
If you want to dig deeper and step through the looking glass you will find that a comprehensive understanding of "Why the universe appears to have one time and three space dimensions?" remains one of the great scientific mysteries of the universe. An article by physicist George Musser in the June 2010 Scientific American Magazine ["Twistor Theory Reignites the Latest Superstring Revolution"], reminded us that: "In the late 1960s the renowned University of Oxford physicist and mathematician Roger Penrose came up with a radically new way to develop a unified theory of physics. Instead of seeking to explain how particles move and interact within space and time, he proposed that space and time themselves are secondary constructs that emerge out of a deeper level of reality. ..." Andrew Hodges of Oxford says that "This idea of points of spacetime as being primary objects is artificial."
Alternate theories where space and time are minor players in our physical reality are still very tentative and so mathematically dense that even those physicists directly involved in developing them admit they can barely follow what is going on. Theorists have yet to explain why, if spacetime is merely a construct, it nonetheless seems so real to us. We include links to articles that suggest what SpaceTime, Relativity, and Quantum Physics may look like in the future. (The Future of Fundamental Physics is a great article that explains some of the problems with current theories. You may want to read it after using the links to get a basic understanding of SpaceTime)
You need to start by watching the PBS Nova series, The Fabric of the Cosmos. It offers an entertaining summary of current theories. You can download NOVA broadcasts from the Apple iTunes store (4 HD episodes for $9.99), or buy the DVD version, or watch streaming episodes online (free) by clicking this link:
The Fabric of the Cosmos .
If you are interested in an overview of Einstein's discoveries take a look at this video.
Another excellent place for students to start is the University New South Wales award winning website Einstein Light (beginner - intermediate).
Because it requires Adobe Flash for the animations you may have to click here to go to the website and enjoy "the finer points of relativity in less time than it takes to eat a sandwich"(Scientific American 2005)
Surprisingly there are not many good videos that explain Einstein's relativity. The following video is a bit boring and incomplete, but it does make some of the basics clearer than other sites.
Here is our list of some of the best Websites [HR - means Highly Recommended / HR bold title is Highly Recommended and at least fairly easy to read]. If you are just beginning to explore the world of modern physics and cosmology, or if you want to do some advanced research on space-time, special and general relativity, quantum physics, quantum gravity, loop quantum gravity, Albert Einstein, space-time warps, time travel wormholes, or similar topics, you will want to visit the websites.
We are not able to carefully read, and therefore do not necessarily agree or disagree with, the content on any internet websites linked to below, including advertising on our site.
If a web link is broken you should still be able to find the pages referred to by using a search engine.
Spacetime HR WikiPedia entry on Space and Time (beginner)
Einstein for Everyone HR Excellent Introductory Text for Students (beginner)
SpaceTime A simple explanation of SpaceTime (beginner - intermediate)
SpaceTime Warps A discussion of SpaceTime curvature and Time Travel (Large 5 meg PDF file) (intermediate - advanced)
Alternative Theories - An Atemporal Universe?
Forget Time HR An essay that discusses the very existence of Time (beginner - intermediate)
What Makes Time Special HR An essay on what we may lose if Time does not exist (beginner - intermediate)
Reflections of Relativity HR 700 page Textbook - Great way to learn about Relativity and SpaceTime (intermediate)
Special Relativity WikiPedia entry (beginner - intermediate)
Graphic Representations of Relativity
Special Relativity Nice graphics, fairly straightforward explanations (intermediate)
The Light Cone - An Illuminating Introduction to Relativity An entertaining selection of graphic views of relativity - some links don't work(beginner - intermediate)
Relativistic Flight Through Stonehenge Entertaining demonstrations (intermediate)
C-Ship A cool graphics site (beginner - intermediate)
Sites for Physics Students
History of Physics - American Institute of Physics (beginner)
Cambridge Relativity Overviews of many current topics in physics and cosmology (beginner - intermediate)
UseNet Physics FAQ An excellent summary of basic questions in general physics, with bibliography (intermediate)
The Equivalence Principle as a Stepping Stone from Special to General Relativity: A Socratic Dialog HR Introduction to General relativity (intermediate)
General Relativity Math Course HR An overview of the math behind General Relativity (intermediate - advanced)
The Meaning of Einstein's Equation A relatively simple introduction to the fundamental geometric nature of the theory of general relativity
Science articles at LANL archive Great source for preprints of science journal articles(advanced)
This Week's Finds in Mathematical Physics Great physics newsletter that offers interesting links (advanced)
The following three videos are from a movie "Down The Rabbit Hole". We were really hesitant to feature them because the movie was sponsored by a "cult", Ramtha's School of Enlightenment, whose founder claims to channel a 35,000-year-old being called Ramtha the Enlightened One. However the video clips we selected are really good at explaining quantum effects. Please do not think that the new age spirituality in the film is based on physics and is more than a myth, in other words ignore everything in the movie except the video clips (even they are slightly wrong).
Dr. Quantum and the Double Slit Experiment from WTB on Vimeo.
Dr Quantum and Entanglement from WTB on Vimeo.
Dr Quantum visits Flatland from WTB on Vimeo.
100 Years of the Quantum HR Excellent 2001 Scientific American Survey of Quantum Physics (beginner - intermediate)
Matt Strassler's - Of Particular Significance HR A comprehensive look at Quantum Theory, worth the effort it takes to find answers on the site (beginner - intermediate)
Particle Physics Excellent Chart of what we know about Matter & Energy (beginner - intermediate)
Quantum Mechanics WikiPedia entry (beginner)
Quantum Entanglement Quantum Entanglement Experiments - a challenge to classic relativity (beginner)
What is Quantum Physics? Simple overview of Quantum Physics (beginner)
Where We Stand Excellent overview of current state of Quantum and Relativity Theories - includes some math (beginner - intermediate - advanced)
Quantum Field Theory HR Excellent overview of QFT by Cambridge Prof David Tong (intermediate - advanced) Here is an excerpt from the Introduction:
The concept of wave-particle duality tells us that the properties of electrons and photons are fundamentally very similar. Despite obvious differences in their mass and charge, under the right circumstances both suffer wave-like diffraction and both can pack a particle-like punch.
Yet the appearance of these objects in classical physics is very different. Electrons and other matter particles are postulated to be elementary constituents of Nature. In contrast, light is a derived concept: it arises as a ripple of the electromagnetic field. If photons and particles are truly to be placed on equal footing, how should we reconcile this difference in the quantum world? Should we view the particle as fundamental, with the electromagnetic field arising only in some classical limit from a collection of quantum photons? Or should we instead view the field as fundamental, with the photon appearing only when we correctly treat the field in a manner consistent with quantum theory? And, if this latter view is correct, should we also introduce an “electron field”, whose ripples give rise to particles with mass and charge? But why then didn’t Faraday, Maxwell and other classical physicists find it useful to introduce the concept of matter fields, analogous to the electromagnetic field?
The purpose of this course is to answer these questions. We shall see that the second viewpoint above is the most useful: the field is primary and particles are derived concepts, appearing only after quantization. We will show how photons arise from the quantization of the electromagnetic field and how massive, charged particles such as electrons arise from the quantization of matter fields. We will learn that in order to describe the fundamental laws of Nature, we must not only introduce electron fields, but also quark fields, neutrino fields, gluon fields, W and Z-boson fields, Higgs fields and a whole slew of others. There is a field associated to each type of fundamental particle that appears in Nature.
Quantum Field Theory - Stanford Encyclopedia of Philosophy Another excellent overview for those interested in a basic understanding of QFT (beginner- intermediate)
Three Interesting Articles by a MIT Professor
The Universe is a Strange Place A look at some of the amazing implications of Quantum Physics (beginner- intermediate)
Quantum Field Theory Another easy to understand overview of Quantum Physics (intermediate)
A Long View of Particle Physics How QFT may explain Matter (intermediate)
Quantum Cosmology a pre-print chapter from Beyond the Big Bang, edited by R. Vaas (Springer, Berlin, 2008) (intermediate - advanced) Here is an excerpt from the chapter:
Quantum cosmology is the application of quantum theory to the universe as a whole. At first glance, this may be a purely academic enterprise, since quantum theory is usually considered to be of relevance only in the microscopic regime. And what is more far remote from this regime than the whole universe? This argument is, however, misleading. In fact, quantum theory itself argues that the universe must be described in quantum terms. The reason is that every quantum system except the most microscopic ones are unavoidably and irreversibly coupled to their natural environment, that is, to a large number of degrees of freedom coupling to the system; an example would be a small dust grain in interaction with air molecules or photons. There exists then only one quantum state which entangles system and environment. The environment is itself coupled to its environment, and so on, leading ultimately to the whole universe as the only closed quantum system in the strict sense. It is entanglement with macroscopic degrees of freedom that also leads to the classical appearance of macroscopic bodies, a process known as decoherence. Decoherence is well understood theoretically and has been successfully tested in a variety of experiments. The universe as a whole is thus at the same time of quantum nature and of classical appearance in most of its stages. There exist, of course, also situations where the latter does not hold and the quantum nature discloses itself; these are, in fact, the most interesting situations, some of which we shall discuss in the course of this article.
Conceptually, quantum cosmology is therefore not necessarily associated with quantum gravity. However, since gravity is the dominant interaction at large scales, any realistic framework of quantum cosmology must be based on a theory of quantum gravity. Although there is not yet an agreement on which is the correct theory, there exist various approaches such as quantum general relativity and string theory.
Discussion of current state of Quantum Gravity, String and Loop Theory Comprehensive article discussing alternative viewpoints (beginner - intermediate)
Quantum Gravity - Cambridge University Press An excellent, somewhat controversial, book by Rovelli on the current state of Quantum Gravity theories, Loop Quantum Gravity, and the implications for space-time (advanced)
String Theory HR - A very good overview of String Theory. Author Patricia Schwarz enthusiasm and communication skills provide a good introduction to strings (beginner).
String Theory - WikiPedia's explanation of the theory. (beginner - intermediate)
Critical Look at Strings - A 2011 article by Rovelli that discusses the strengths and weaknesses of string theory. (beginner - intermediate)
The Trouble With Physics - review - String Theory is by far the most popular theory. There appears to be a common thread to the quest for alternatives to String Theory that focuses on electromagnetism and relativity with a form of gauge theory, quantum electrodynamics, and topological quantum field theory. Only time will tell if an background free atemporal alternative will be found. (beginner)
Loop Quantum Gravity - Rovelli's overview of the first 25 years of LQG. (beginner - intermediate)
Being and Becoming in Modern Physics Excellent article on SpaceTime Metaphysics in the Stanford Encyclopedia of Philosophy.
Absolute Being and Relative Becoming Interpretation that harmonizes the atemporal block universe of Relativity with the temporal model of Quantum Physics
Physics Meets Philosophy at the Planck Scale Pre-print of chapter by Carlo Rovelli that outlines his views, which we basically agree with, on Space and Time
Christians in Science A thoughtful exposition of the compatibility of religion and science from professors at the University of Cambridge, England
Center for Theology and the Natural Sciences One of several relevant sites affiliated with universities
SpaceTime is Sponsored by our philosophy and religion site LifeNotes. Please visit our site:
Einstein’s theories of relativity tell us that Space, for example - the room you are sitting in, and Time, the minutes that tick away on your watch, are all part of a single physical entity, the SpaceTime Continuum. SpaceTime has four dimensions, roughly corresponding to east-west, north-south, up-down, and past-future. We can drive from east to west, north to south, and go up and down mountains. While we are driving in any direction we are always driving from our past to our future – that is basically why space and time are linked, we can’t move through space without moving through time!
Before Einstein, Isaac Newton shared the popular belief that both absolute time and absolute space exist. Newton believed that the grid that defined absolute space was undetectable, but that there is a universal time that ticks away for all observers in all locations, and that universal time can be accurately measured by clocks. If it is 5 o'clock on planet earth, it is simultaneously 5 o'clock on the most distant star. Similarly, Newton believed that absolute space exists that can be measured using the same yardstick (meter-stick) anywhere in the cosmos, a mile measures the same distance anywhere on Earth and on any distant star as it does where you are standing right now.
There are lots of problems with this idea, experimental observations simply do not support the conclusion that absolute time and absolute space exist. In 1905 Einstein published his theory of special relativity, which introduced the then radical idea that different observers see the same event occurring at different times and places. For example, Bill and Sally may see two firecrackers that they ignite explode at exactly the same time, while Jane (in motion at a distance) may see one of the two firecrackers explode a few seconds before the other one.
Einstein used the concept of relationships between frames of reference to explain how these "crazy" observations are real and actually do occur. Frames of reference may be thought of as invisible "coordinate map grids", like the letters and numbers on the sides of roadmaps, attached to every observer so that the observer can measure the position of surrounding objects.
Special relativity tells us that observers who are in a state of uniform motion with respect to one another are in "inertial frames of reference", and that they cannot use the laws of physics to distinguish the frame of reference of one observer from the frame of reference of any other observer. In an inertial frame of reference, there is no physical experiment whatsoever that you can perform that can distinguish between a state of rest and a state of constant velocity (if you are going down in an elevator, a ball released from your hand does not fly to the ceiling). If you are in a windowless room, there is no experiment that you can perform in that room that will tell you if the room is stationary, or is moving in some direction at a constant velocity, or is in uniform "free fall" acceleration.
Think about being in a silent electric car with all the windows painted black (you can’t see out so you can't tell if you are moving relative to the road and you can’t listen to the engine for clues about your speed). If the car is standing at a red light, and you put a coffee cup on the dashboard, the cup will not move. If the car is going a steady 120 miles an hour (you did not feel the acceleration because you were asleep), and you put the cup on the dashboard, the coffee will not fly back and hit you in the face. There is no experiment that you can do inside the car (which is your inertial frame of reference) that will tell you if you are standing at a red light, or going down the road at 90 miles per hour, or even 90,000 miles per hour! What happens when a car accelerates smoothly after the red light turns green? The same thing that would happen if the car fell (smoothly) off the edge of a cliff, as the car falls toward the ground below the coffee will still remain in the cup on the dashboard (until you reach the valley floor).
Note that Newton's first law of motion, which in essence states that an object in motion will remain in motion unless acted on by an external force, is consistent with this result at lower speeds. So long as Newton's laws are applied only where relative velocities do not approach the speed of light, Newton's laws of motion give us "close enough" results, even in a relativistic universe. That is why they are still taught in schools as "true" physical laws.
You cannot determine if the car is moving at constant velocity, or is standing still, or is in a uniformly accelerating gravitational free fall. That does not mean that you cannot determine non-uniform acceleration. If you press the accelerator so that the car "speeds up", or if you swerve from a straight path, you will feel the acceleration and be able to measure it (the coffee cup will fly off the dashboard). None-the-less, there is no physical experiment whatsoever that can distinguish between a state of rest, a state of constant velocity, and a state of gravitational free fall. Our solar system is located on a spiral arm of the Milky Way galaxy, which rotates at a constant velocity (creating a nearly inertial frame). If we did not live in inertial frames, and we could do an experiment to measure the motion, then every time we got out of bed the speed of our earth / solar system rotating around the Milky Way (about 155 miles/sec or 250 km/sec) would knock us to the floor! Every time we set the coffee cup down in our moving car, the coffee would hit us in the face!
One startling conclusion that we reach from all this is that the velocity of light must have the same value for all inertial observers, even if they are moving toward or away from the source of the light. If this was not true, an observer could perform an experiment using a beam of light to measure the velocity of their inertial reference frame, and then use that result to determine which of several frames of reference (frames in constant motion) they were actually in. The disastrous results of a speed of light that is additive (not constant in all frames) would include being hit in the face by the coffee, and, even worse, being plastered to the floor by the speed of the earth flying through space.
Experimental results fully support the counterintuitive predictions of special relativity. Clearly, the idea that the speed of light is constant is inconsistent with an absolute space that is distinct and separate from an absolute time. Modern physics replaces Newtonian space and time with a single entity, Space-Time. Minkowski, who along with Einstein formalized the math of Spacetime, said, "…henceforth, space by itself, and time by itself, have vanished into the merest shadows and only a kind of blend of the two exists in its own right."
Space-time is essentially a "curved" geometric construct that allows for the relativity of simultaneity. In other words, if one observer correctly concludes that two events occur simultaneously, the same events would appear to take place at different times to an observer who was in motion relative to the first observer. Both the observer who measures the two events to be taking place simultaneously, and the observer who measures the events as taking place at different times, are right! Our example above is correct, one observer will see a firecracker they light and a second firecracker that a friend lights explode at exactly the same time, while a third observer moving relative to the other two will see one firecracker explode before the other firecracker. Relativity tells us that both are right!
Both time and space are relative, and are "different" for observers in relative motion to one another. For one observer the two firecrackers actually did explode at precisely the same time, while for the other observer one firecracker exploded a few seconds before the other. The time and distance measured by each observer is different, both are right, neither is wrong!
Relativity tells us that time and distance change depending on the relative motion of the observers. If Observer A measures the passage of one hour on their clock, another observer B who is in relative motion to observer A may measure the passage of 30 minutes on the clock. If Observer A measures a distance of one mile on their ruler, another observer B who is in relative motion to observer A may measure a distance of 1/2 mile on the ruler. We don't see time or distance shrinking on earth because the effect is virtually undetectable until the relative motion of two observers approaches the speed of light (299,792.458 kilometers or 186,000 miles per second). None-the-less, the time and distance measured by two observers in relative motion to each other is different, only the speed of light measured by all observers is the same.
Einstein-Minkowski space-time is made up of three spatial dimensions x, y, and z, and one time dimension t. Space-time is commonly thought to be the history of the entire universe, containing every "event" that ever happens. A "world-line" is the history of an object in "space-time".
Special relativity allows us to define a distance from the origin for all the points on a world-line, allowing the world-line to be a set of points that have physically distinguishable properties. Therefore, we can identify each of the events on a world-line as distinct points in space-time. Each point on the world-line is a particular event that happens at one place in space (represented by the values of the x, y, z coordinates) at one particular time (represented by the value of the t coordinate) - i.e. one place in space-time. Each point on the world-line of a human being is generally thought to be a real physical event that represents a unique sequential moment in the life of that individual, from birth to death.
Einstein said “Imagination is more important than knowledge”. So to better understand what we are talking about set your imagination free and take a journey with me into space-time. First there is an underlying question, if we travel to the end of the universe and find a brick wall, what is behind the wall? Is our universe inside a walled "container" that might allow us to measure distances from points on the fixed surface of the container? Or is our universe the container itself with nothing beyond the boundaries? If so then there is no fixed background we can use to measure time and space. Einstein's General Relativity favors a background free universe where distance and time are measured by relative positions of objects in our universe, Quantum Theory favors (but does not necessarily require) the existence of a complex, yet still fundamental, time.
To better understand Einstein's view of spacetime imagine a universe that is totally empty except for one single ball. There is absolutely nothing else in the entire universe, no atoms, no rocks, no people, just a single ball we will call ball “A”. The ball is floating in totally empty space, there is no background behind it, no horizon, nothing. How far is the ball from anything else in this one object universe? There is no answer, because the ball is the only object in the universe, so there is absolutely nothing else in the universe that we can measure a distance to, not even some kind of background like a sky full of stars (we ignore the complex issues of rotation and frame dragging in our examples).
Now add a second ball "B" to our universe.
How far is it from ball A to ball B? We reach for a ruler – but wait – remember that the only two objects in the entire universe are the two balls, there are no other objects, no rulers, not even a background grid to measure against! Just two balls floating in nothing.
Here we can see the problem - since there are only two objects in the entire universe, ball A and ball B, there is no ruler you can go get to measure the distance between ball A and ball B. There is no way whatsoever to measure the distance between A and B because there is nothing to compare the positions of the balls to. So it seems that we must conclude that there is “separation” but there at least appears to be no such thing as "distance" in this two object universe.
Add a third ball "C" to the universe (remember there are three objects A, B, and C in the universe and absolutely nothing else).
Now if we ask how far it is from A to B we can at least make an imaginary ruler using the distance of B to C:
and then measure the distance from A to B using our new ruler:
By comparing the distance from A to B to the distance from B to C – we see that the separation between A and B is five times greater the separation from B to C.
Remember – you are looking at these drawings on a computer screen or on paper. The screen/paper gives us an extra “object” that really does not exist in our one, two, and three ball universes. There is no background in our examples, the balls are simply suspended in empty space. As you read remember, and imagine, that there is no screen, no paper, no background – the balls simply float in absolute nothingness.
We could have chosen to build our ruler using the distance from A to B instead of B to C:
then the distance from B to C would have been 1/5th the distance from A to B.
We can ask what the distance is from A to B by comparing it with B to C - and say that it A to B is 5 times the distance from B to C, or we can ask what the distance is from B to C by comparing it with A to B - and say that B to C is 1/5th the distance from A to B.
What we have done is to choose A to B or B to C to be our "ruler". That is what we human beings do when we build a "meter" (or a "yard") stick, we define the distance from end of a wooden stick (A) to the other end (B) to be one meter (yard) so we can use it to measure the distance between any other points in the world.
Because we are using endpoints A and B that we arbitrarily chose to define a meter (yard), we are comparing the distance from endpoint A to endpoint B and endpoint B to endpoint C, just like we did with the three balls in the three object universe.
Now crank up your imagination a couple notches. What if the balls looked like this in Universe X -
instead of like this in Universe Y:
Wait a minute – we said there is no paper in our three ball universes, no backgrounds to measure against. So if we measure A to B using B to C we get the very same answer in both universes – the “distance” from A to B is Five times the “distance” from B to C. Since the balls are floating in absolutely empty space, there is no background, no horizon, no grid, we can use to measure an absolute distance between A and B and B and C. There is no way to tell if we are in Universe X or Universe Y. If we see three balls and measure the distance from A to B to be 5 time the distance from B to C:
Are we in Universe X or Y? We absolutely cannot tell. In Universe X we measure the distance from A to B to be 5 time the distance from B to C, and in Universe Y we measure the distance from A to B to be 5 time the distance from B to C – there is nothing we can measure that will tell us which Universe we are in. (Our example is actually physically impossible because we cannot distinquish between the lengths of units in Universe X and Y, we hope it helps you see why no experiment could compare the two rulers)
What all this tells us is that what matters is the relative position of objects in the universe, not the absolute position, because there is no absolute position. We measure the relative position of objects and that allows us to measure the relative distance between two objects. That is what relativity is all about, there is no absolute distance because there is no background, no “piece of paper”, to measure absolute distances against.
Everything would be pretty simple if relative positions never changed:
but they do change, constantly, because objects are in “motion” and “motion” means change in relative position:
Use your intuition to realize that for every change in the relative position of A and B there is a physical limit on the change in relative positions of A, B, and C – in other words there is a physical limit on the speed in which objects can move away from each other. It is a tiny bit like the fact that when you get in your car to go to the grocery and step the accelerator to the floor, there is a physical limit on the change in how far you are from your house and how close you are to the store. No matter how hard you press the accelerator the speedometer will never reach 500 miles per hour, and it will always take you a minimum length of time to get from your house to the store.
In the universe in which we live there is a physical limit on the change in relative position of all objects, including balls A and B and C, it is called the “speed of light”. Light can be thought of as being little balls of energy called photons (I know we are oversimplifying and the descriptions are really not right – but they illustrate our points). Assume ball C is a photon “ball”. Because of physical limits on the change in relative positions, i.e. on the speed the three balls can separate from each other, ball A and ball B can never move apart (change relative position) so that the change in relative position between ball A and ball B is greater than the change in relative position between ball A and photon C or ball B and photon C. A and B can never speed apart from each other so that they go faster than a photon speeding away from A and B. The speed of light is a physical limit on the motion of every object that is part of our universe, period.
Now here is where it gets weird, or weirder. Instead of three balls in an empty universe, let’s look at John, his brother Henry, and their friend Marge. John is having his morning cup of coffee with Marge at the local café. His brother Henry is back at the house where both live.
John and Marge leave the café and get on their “Speed-o-Lite” rocket motorcycles. Both start driving off away from Henry at almost the speed of light. Henry waves good-bye. So far no problem.
Relative to Henry, John and Marge are speeding off (changing relative position) at almost the speed of light – but John and Marge are driving beside each other so they are not moving apart at all. If the roadway is smooth, John could hand Marge a cup of coffee and she would not spill a drop.
A police officer sees John and Marge fly by and measures their speed to be just under the intergalactic speed limit, 299,792.5 kilometers per second (It has been correctly pointed out to us that a stationary police officer at Henry's house must view the moving clocks on John and Marge's motorcycles through a telescope, or wait until they bring the clocks back to Henry's house, to determine their relativistic time and distance and calculate their speeds).
Marge wants to try out her new bike, so she pushes the accelerator and shoots ahead of John – pulling away from John at almost ½ the speed of light – wow!!!!!
So John is moving away from Henry at almost the speed of light, and Marge is moving away from John at ½ the speed of light, Marge must be moving away from Henry at 1 and ½ times the speed of light – right? The police officer thinks so, and gets ready to write Marge a speeding ticket.
Wait a minute, we said that the physical limit on how fast any two objects can move away from each other is the speed of light – so John is moving away from Henry at almost the speed of light and Marge is moving away from John at ½ the speed of light – but Marge must be moving away from Henry at a bit less than the speed of light????? I am confused?
This is where space-time takes over, and keeps Marge from getting a ticket. Now the amazing thing - the ruler the police officer uses to measure how far Marge and John are from Henry shrinks, and the clock the officer uses to determine how fast Marge and John cover the distance slows down. The result is that the police see both Marge and John speeding away from Henry at less than the speed of light.
Remember that the ruler and clock that John and Henry use to measure John's distance and speed relative to Henry shows John moving away from Henry at 99.999999% of the speed of light, and the ruler and clock that John and Marge use to measure Marge's distance and speed relative to John show Marge moving away from John at ½ the speed of light. None-the-less, the ruler that the Police use to measure Marge and John's distance relative to Henry shrinks (talking about rulers makes things less intuitive than talking about the actual measurement - the Police measure the distance Marge travels as just enough less than what they would see if she was going faster than the speed of light - she is traveling a shorter distance) and the clock slows down just enough (the Police measure that it takes just enough more time for Marge to travel the distance than they would see if she was going faster than the speed of light - she is going slower) so that Marge is not breaking the speed laws of Physics, she is not going faster than the speed of light relative to Henry or anyone else!
This is why distance and time depend on the relative position and the change in the relative position, not absolute position, of objects. If distance and time did not change depending on the relative positions of objects in motion, those objects could move apart at speeds greater than the speed of light, the physical limit no object can exceed, and the world would be an even weirder place than it is. If you are having trouble visualizing time and space dilation click on this link to Einstein Light for excellent (Adobe Flash) animations. Once you understand the concept of measurements being relative, the idea of rulers shrinking, and clocks going slower, is not as strange as it might seem. This is what Space-Time is all about!
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