"Time is the speed of light."

[Lois]

Today the chairman of the club had a familiar inventors and said from the rostrum of tremendous phrase: "Time is the speed of light." If you have any comments?

[Michael Sternbach]

That's why as things move through space, their time flow slows down. The faster their movement through space, the slower their movement through time. It's a trade-off. If they could reach the speed of light, the time flow they experience would stop entirely. That's what Einstein showed.

[Nungali]

I want to stand on that 'rostrum of tremendous phrase '  ( so I can see what comes out of my mouth  )    

[Apech]

Time is money.

[Nungali]

So , time is evil ? 

[Nungali]

~   If it wasnt for that rather serious other thread ... where I am not game to say anything ....  I would have enough real estate in OT to buy a motel .  But I just cant seem to get there  

[haedon]

I want to believe that that is how time is measured.

[Basher]

Money, rather like a Gun, isn't evil in and of itself.

I believe that the line goes "The Love of Money, is the Root of all Evil".

But I'm not even sure that I agree with that.

 

Plenty of the World's Billionaires are spending a large proportion of their collective Fortunes on helping others & various good causes. Before judging them, how much of your time / salary do you give freely to benefit others ?

 

Tempus Fugit (or something like that)

[Michael Sternbach]

Here is a 1000 $ question to you guys: What has money got to do with the speed of light? Right - absolutely nothing! Let's try to get back on topic then...

 

So, the OP states that time is the speed of light. I demonstrated above that this must be correct, in essence, as an object spatially at rest moves through time at c. However, this statement is not without difficultiess, since c is defined as about 300'000 km/sec, which obviously describes a movement through space.

 

At what pace does something move through time? Well, in the most simple scenario, at 1 sec/sec. But accelerate it to a velocity near c, and its time flow will be reduced to a mere fraction of a second per second, as measured by the external observer. As I explained, that occurs because some of its movement through time is being transformed to movement through space. However, time flow as experienced by the moving object itself hasn't changed! Instead (again subjectively or relatively speaking), its movement in space now far exceeds the speed of light! (In my understanding, at least.)

 

That's why a space ship travelling at a velocity very close to c could traverse the roughly two and a half million light years to the Andromeda galaxy in something like 25 years - 25 of its own years, of course, while in the outer universe two and a half million years would pass...

 

Obviously, the relationship between the different space-time frames as described by Special Relativity is somewhat mind boggling. Perhaps Brain, um, Brian could shed some more light on this topic - in simple Dao Bums terms?

[Jeff]

I would argue that the speed of light is a very limited concept based in "time and space".  The concept of quantum pairing sort of shows that it is really not a limit.

[Marblehead]

My mind can travel faster than the speed of light.

[Brian]

When people tell me they can't find the time for something, I tell them that's easy! (Well, except for the hard part...)

 

First, find space. (Hint: this will work better for you if you stick to Cartesian coordinates)

 

Notice that the three dimensions (sometimes called "X" "Y" and "Z" because they're in a witness protection program) are each at right angles to the other two (mathematicians might call them "orthogonal" because that sounds more impressive.

 

Now, look in the direction at a right angle to all three of them at the same time. Yes, this is the hard part.

 

Now turn around. Time is right behind you!

 

 

OK, seriously.

 

Shortly prior to Einstein's famous year of 1905 (we should talk about his first wife at some point...), a Dutch physicist named Hendrik Lorentz made a remarkable discovery. Well, we should back up just a bit.

 

Let's go back to 1687...

 

Isaac Newton (a natural philosopher) established three laws of motion and fleshed out the mathematical machinations necessary to describe the motion of objects. Most people are at least vaguely familiar with the laws -- we typically state them something like this:

1) A body at rest tends to stay at rest, and a body in motion tends to stay in motion at a uniform velocity, unless acted upon by an external force,

2) An object acted upon by an external force will accelerate at a rate proportional to the force and inversely proportional to its mass (Sorry! You're probably more familiar with it flipped around as F=ma),

3) For every action, there is an equal and opposite reaction.

 

But wait! Let's go back to 1632 for a moment. Galileo explained that the laws of motion are the same regardless of the inertial frame of reference used. An inertial reference frame in this context sounds complicated but it is really that which with we are most familiar -- imagine an XYZ coordinate system that isn't spinning (or that we can pretend isn't spinning for the purposes of our work) and isn't accelerating (this means it can be moving but in a straight line at a constant speed). So, up-down-left-right/forward-backwards works great if you are standing on solid ground or riding on a cruising train but not if you are spinning around on a turntable. According to Galileo, the description of a ball thrown in the air from the perspective of someone riding on the train is exactly the same as the description of the motion of the ball from the perspective of someone standing on solid ground as the train goes by -- as long as the uniform motion of the train is taken into account.

 

Galileo was onto something but his laws of motion were kinda wonky.

 

Newton came along right after him and gave us the set we use now for virtually everything we do or experience regarding forces and motion. Galilean invariance (fancy way of saying the laws of motion don't change just because you hop on a train) works perfectly with Newton's laws.

 

Then along came Maxwell (yeah, we are skipping a bunch of people in between...)

 

James Clerk Maxwell was a Scottish physicist and mathematician. That doesn't do him justice, though, as he was a genius in multiple disciplines, including poetry, literature, scripture, optics, thermodynamics, hydrostatics, eningeering -- pretty much anything for which he developed a curiosity. He became the Dean of Natural Philosophy at Marischal College in 1856.

 

Maxwell is most famous for the work he did on electromagnetism. Specifically, he synthesized the works of Ampere, Gauss and Faraday and, with his own modifications and additions, introduced in the 1860the set of equations physicists and engineers still use for describing electricity, magnetism and the curious creature we call electromagnetism.

 

What in the world does this have to do with space-time, you might ask? Well, as a necessary outcome of these equations, Maxwell realized that electromagnetism propagates at the same speed as light, and he further realized this wasn't a coincidence. Additionally, he discovered that he could use existing data to calculate the speed of light. On top of that, he demonstrated that the speed of light was invariant -- that it was the same regardless of the inertial frame of reference used to measure it.

 

Think about that for a moment. No matter whether you were moving in the direction the electromagnetic wave was moving or you were moving in the exact opposite direction, you would measure the speed of the wave to be the same. This is totally alien and foreign to our experience but it is not only easily demonstrated, it is predicted by the mathematics. Question then became, what does all this mean?

 

So, back to Lorentz.

 

Along with a bunch of other natural philosophers (it is about this time that the term "physicist" started to replace that phrase), Lorentz was exploring the consequences and implications of Maxwell's equations. One of the things he was playing with was to see if he could find a way to make the laws of electromagnetism invariant in the same way that the laws of motion are invariant. What he discovered was that the introduction of the term "-c²t" made everything happy.

 

So, instead of just dealing with X, Y & Z, Lorentz discovered that we were really dealing with X, Y, Z and c²t. Mathematically speaking, this new time-based term behaves EXACTLY like the more familiar space-based terms and doing transformations between inertial frames of reference with electromagnetism was just like doing them with the motion of physical objects, only slightly more messy because you had to work with four dimensions instead of three.

 

Now, let's step forward another 15 years or so. Two young physicists named Einstein (remember I mentioned Albert's wife?) had an extraordinary year. In 1905, known as "Annus Miribilis", Einstein published four important papers.

 

The first showed that electromagnetism is not smooth "stuff" but is actually little bundles of energy which come in various discrete "sizes" (size is not really the right adjective because it suggests physicality but we'll leave that alone for now. This was an extension of the work by Max Planck but marked the introduction of the term "energy quanta." This paper also explained how light could be generated directly from flow of electrons (as opposed to just heating a wire until it is hot enough to glow) and that the reverse was also true -- electrons flowing because of electromagnetic waves. This is the paper which later earned Albert a Nobel Prize (the money for which he gave to his now-ex-wife).

 

The second paper was an explanation of Brownian motion -- the way particles in a fluid (either liquid or gas) jiggle and bounce around. The phenomenon was well documented and could be seen with a microscope but was not understood. This paper not only provided a mathematical model for this phenomenon but it also drove a stake in the idea of matter being smooth "stuff" and solidified (pun intended) the atomic model.

 

The third was special relativity. I'll come back to this one in a moment.

 

The fourth was on mass-energy equivalence. This paper showed that a particle has not only classical "potential energy" and "kinetic energy" but that the very concept of "mass" is an expression of energy, too. It is in this paper that the famous but rarely comprehended "E=mc²" equation is introduced.

 

But back to special relativity...

 

Galileo showed that motion is relative but didn't get the laws of motion right. Newton fixed that and gets credit for classical "Newtonian relativity" which works beautifully until things get to speeds approaching the speed of light. The Einsteins explained why (or, at least, offered a predictive, consistent and testable model which turned out to work very nicely. The reason it is called "special relativity" is because it is limited to a particular set of conditions, namely the same inertial frames of reference used by Newton. By applying the exact same Lorentz transformation (remember that "-c²t" fourth dimension Maxwell incorporated in his equations for electromagnetism?" to Newton's laws of motion, it was demonstrated that energy, mass, space (distance) and time are all interconnected AND showed that electromagnetism and the motion of physical objects are perfectly consistent with each other. At its core, special relativity says that everything is relative EXCEPT the speed of light. It is important to remark that special relativity is confined to inertial frames and to note that it necessarily neglects gravity. (Einstein would eliminate those two restrictions ten years later with "general relativity.")

 

I take the time to step through all this to demonstrate that "relativity" didn't just appear out of the blue (as seems to be a common misconception) but was a natural development springing from a couple hundred years of incremental advances by a bunch of really smart folks.

 

There are some peculiar implications of special relativity (and some even stranger ones from general relativity which contains all of special relativity plus much more, but we'll stay away from them for now...)

 

One that causes people headaches is that special relativity destroys the concept of simultaneity. That is, given any two events, A & B, separated by any distance, whether A happens before B, or B happens before A, or A and B happen at the exact same time it totally dependent on the observer's frame of reference. In fact, the concept of "at the exact same time" loses meaning because measuring time is a relative thing.

 

Another necessary implication of special relativity is length contraction. This says that, when an inertial frame of reference (and, by extension, an object being measured against that coordinate system) is moving, it gets "squished" along the direction of motion. The dimension of space literally contracts or gets compressed.

 

A fourth implication of special relativity is the equivalence of energy and mass. This one builds upon the E=mc² principle and it means that the apparent mass of an object depends on how fast it is moving. I say "apparent mass" not because it is an illusion but because mass is a relative thing, too -- how massive an object is depends on the relative motion between the object and the observer's inertial frame of reference.

 

A fifth implication (and this is the one you have been waiting for) is time dilation. If you take two identical clocks (the design and mechanics of the clock are irrelevant), synchronize them to the n^th degree, put one on a fast jet and fly it around the world, and then bring them back together again, you will find that the fast-moving clock slowed down. This is not a mechanical artifact of the design or construction of the clock and can be demonstrated in lots of other ways, too, but this "fly a clock around the world" approach has actually been tested. What special relativity predicts and requires, and what oodles of experiments have confirmed over and over, is that time literally gets "stretched out" or dilated. The amount to which it "slows down" is precisely described by Newton's laws of motion modified to include the Lorentz transformation and time gets slower and slower (or longer and longer, depending on how you want to look at it) depending on the relative speed between the observer and the object being observed. In fact, as the relative speed approaches that invariant "speed of light," the "length" of a time period (a "second" or "minute" or whatever you'd like to use) approaches infinity. Another way of stating that is to say the rate at which time ticks by gets slower and slower, until, as the speed approaches the speed of light, time grinds to a halt.

 

We say it takes eight minutes for light to travel from the Sun to the Earth (a distance of 93 million miles at a rate of 186k mph). If we could build a ship that rapidly accelerated to very, very nearly the speed of light and we sent it towards the Sun, an Earth-based observer would see it took just slightly over eight minutes to get there. For the passenger on the ship, however (assuming that person could somehow survive the acceleration), time would be ticking by so slowly that the trip would take practically no time at all -- the second hand on the observer's watch might not even move before the journey was over.

 

When you put the implications I list above together, it becomes apparent that we cannot accelerate an object to the speed of light. Mass goes to infinity and the rate at which you can develop a propulsive force goes to zero. We can approach the speed of light arbitrarily close, though, depending only on our technology. The clear implication, though, is that something somehow moving at the speed of light (like light itself, for instance) experienced no passage of time. In fact, time loses all meaning -- the "time" it takes for a photon to travel from the Sun to the Earth takes eight minutes from the perspective of someone on the Earth but it takes zero time from the perspective of the photon traveling at the speed of light. The "time" it would take for a photon to travel all the way across the universe (as we see it from Earth) would take zero time, too -- from the photon's perspective. At the speed of light, then, the "time" the photon would see on its wristwatch (if photons had wristwatches) at any point along that journey and beyond would be exactly the same. This is indistinguishable from the photon simultaneously being everywhere along that path.

 

Mind-boggling is right.

[Brian]

FWIW, it's a common mistake to think that relativity speaks to FTL or SoL travel. It only addresses acceleration to the speed of light.

[Bud Jetsun]

http://www.natureworldreport.com/2015/10/quantum-entanglement-all-but-confirmed/

 

 

 

Clocks are boxes of cogs or arrangements of silicon.

 

Time remains an artifact of human perception limitation.

 

Rate implies a distance over time. There remains Oness and human perception limitation induced confusion as to the nature of reality when the Oneness appears as a collection of separates.

 

Unlimited Love,

-Bud

Edited November 19, 2015 by Bud Jetsun

[MooNiNite]

if one's awareness vibrates faster than light, "body of light", perhaps they transcend time, becoming immortal.

[Nungali]

if one's awareness vibrates faster than light, "body of light", perhaps they transcend time, becoming immortal.

 

 

 

no .. as a vibration higher than light  is gamma rays and they will turn into

 

 

Edited November 19, 2015 by Nungali

[Marblehead]

Great post.

 

I have a problem with this though.

The clear implication, though, is that something somehow moving at the speed of light (like light itself, for instance) experienced no passage of time. In fact, time loses all meaning -- the "time" it takes for a photon to travel from the Sun to the Earth takes eight minutes from the perspective of someone on the Earth but it takes zero time from the perspective of the photon traveling at the speed of light. The "time" it would take for a photon to travel all the way across the universe (as we see it from Earth) would take zero time, too -- from the photon's perspective. At the speed of light, then, the "time" the photon would see on its wristwatch (if photons had wristwatches) at any point along that journey and beyond would be exactly the same. This is indistinguishable from the photon simultaneously being everywhere along that path.

Mind-boggling is right.

The speed of light is 186,000 miles per second.  (The same speed RF energy travels.)

 

The photon is light energy.  How can it travel faster than itself?

[Brian]

Great post.

 

I have a problem with this though.

The speed of light is 186,000 miles per second. (The same speed RF energy travels.)

 

The photon is light energy. How can it travel faster than itself?

Light doesn't travel faster than light. Light comes into existence already moving at the speed of light.

 

Special relativity shows that we cannot take an object with mass and accelerate it the speed of light. Not a technology limitation but rather the way the universe works.

 

Special relativity also shows that time slows down as one approaches the speed of light. As one gets closer and closer to the speed of light, the rate at which time passes gets slower and slower. Get infinitesimally close to the speed of light and the rate at which time passes grows infinitesimally close to zero. It is important to note that, even at infinitesimally close to the speed of light, light is still measured as traveling at the speed of light.

 

The takeaway from this thread should be that, at the speed of light, the concept of the passage of time loses meaning. The light wave's clock is stopped.

[Brian]

Indeed. The universe as we currently understand it is indexed to light. My expectation is that this understanding will be expanded, that electromagnetism will be recognized to be a subset of a more encompassing understanding of energy. This index will shift accordingly and the new model will be consistent with the current model as well as providing new understanding. I refer to the fundamental energy which includes light as Light, for lack of a better term.

 

I suspect this process of refining models and introducing increasingly comprehensive and nuanced models to supplant older models is an unending process -- that is to say that I believe one of the fundamental characteristics of the Tao is its intellectual ineffability.

[Marblehead]

The takeaway from this thread should be that, at the speed of light, the concept of the passage of time loses meaning. The light wave's clock is stopped.

Yes, but only for those who are traveling at that speed.  For everyone else time has not changed.  There are still 60 seconds for a minute.

[Marblehead]

There are still some theories which permit universal time....It would suggest, then, that there are higher order structures that still utilize time which can apprehend the disparate frames.

 

I haven't spent much time on it recently but this was something I encountered in the past that could describe some of it:

https://en.wikipedia.org/wiki/Sheaf_%28mathematics%29

 

A take-away is not that time loses meaning but time necessitates a reference point and a locality index or scaling value to help with making sense of things.

But still, the present way we measure time is pretty darned good.  Night comes when it is supposed to and summer comes when it is supposed to.  Our sun and moon seem to be doing a pretty good job at keeping things together.

[Brian]

Yes, but only for those who are traveling at that speed. For everyone else time has not changed. There are still 60 seconds for a minute.

For the person approaching the speed of light (relative to some arbitrary observer), time hasn't changed, either. Pulse rate is the same, still sixty seconds in a minute, half-life of a uranium atom hasn't changed, etc., etc.

 

All observations depend on the observer's frame of reference and, at the same time, the laws of nature seem to be invariant with regards to the speed of light (in exactly the same way that a hit baseball behaves the same whether viewed by a running outfielder or someone sitting in the stands).

[Lois]

but what about the time machine?

 

http://www.fluxcap.com/hdr_hyper_dimensional_resonator.htm

[Brian]

but what about the time machine?

 

http://www.fluxcap.com/hdr_hyper_dimensional_resonator.htm

Just be sure to take off your tin-foil hat first. You can buy an HDR here for only $500 bucks (plus $20 for shipping and handling):

http://www.espionage-store.com/secret/time2.html

 

If they really wanted to impress customers, they would deliver the HDR an hour before the person placed the order!

[Michael Sternbach]

When people tell me they can't find the time for something, I tell them that's easy! (Well, except for the hard part...)

First, find space. (Hint: this will work better for you if you stick to Cartesian coordinates)

Notice that the three dimensions (sometimes called "X" "Y" and "Z" because they're in a witness protection program) are each at right angles to the other two (mathematicians might call them "orthogonal" because that sounds more impressive.

Now, look in the direction at a right angle to all three of them at the same time. Yes, this is the hard part.

Now turn around. Time is right behind you!

OK, seriously.

Shortly prior to Einstein's famous year of 1905 (we should talk about his first wife at some point...), a Dutch physicist named Hendrik Lorentz made a remarkable discovery. Well, we should back up just a bit.

Let's go back to 1687...

Isaac Newton (a natural philosopher) established three laws of motion and fleshed out the mathematical machinations necessary to describe the motion of objects. Most people are at least vaguely familiar with the laws -- we typically state them something like this:

1) A body at rest tends to stay at rest, and a body in motion tends to stay in motion at a uniform velocity, unless acted upon by an external force,

2) An object acted upon by an external force will accelerate at a rate proportional to the force and inversely proportional to its mass (Sorry! You're probably more familiar with it flipped around as F=ma),

3) For every action, there is an equal and opposite reaction.

But wait! Let's go back to 1632 for a moment. Galileo explained that the laws of motion are the same regardless of the inertial frame of reference used. An inertial reference frame in this context sounds complicated but it is really that which with we are most familiar -- imagine an XYZ coordinate system that isn't spinning (or that we can pretend isn't spinning for the purposes of our work) and isn't accelerating (this means it can be moving but in a straight line at a constant speed). So, up-down-left-right/forward-backwards works great if you are standing on solid ground or riding on a cruising train but not if you are spinning around on a turntable. According to Galileo, the description of a ball thrown in the air from the perspective of someone riding on the train is exactly the same as the description of the motion of the ball from the perspective of someone standing on solid ground as the train goes by -- as long as the uniform motion of the train is taken into account.

Galileo was onto something but his laws of motion were kinda wonky.

Newton came along right after him and gave us the set we use now for virtually everything we do or experience regarding forces and motion. Galilean invariance (fancy way of saying the laws of motion don't change just because you hop on a train) works perfectly with Newton's laws.

Then along came Maxwell (yeah, we are skipping a bunch of people in between...)

James Clerk Maxwell was a Scottish physicist and mathematician. That doesn't do him justice, though, as he was a genius in multiple disciplines, including poetry, literature, scripture, optics, thermodynamics, hydrostatics, eningeering -- pretty much anything for which he developed a curiosity. He became the Dean of Natural Philosophy at Marischal College in 1856.

Maxwell is most famous for the work he did on electromagnetism. Specifically, he synthesized the works of Ampere, Gauss and Faraday and, with his own modifications and additions, introduced in the 1860the set of equations physicists and engineers still use for describing electricity, magnetism and the curious creature we call electromagnetism.

What in the world does this have to do with space-time, you might ask? Well, as a necessary outcome of these equations, Maxwell realized that electromagnetism propagates at the same speed as light, and he further realized this wasn't a coincidence. Additionally, he discovered that he could use existing data to calculate the speed of light. On top of that, he demonstrated that the speed of light was invariant -- that it was the same regardless of the inertial frame of reference used to measure it.

Think about that for a moment. No matter whether you were moving in the direction the electromagnetic wave was moving or you were moving in the exact opposite direction, you would measure the speed of the wave to be the same. This is totally alien and foreign to our experience but it is not only easily demonstrated, it is predicted by the mathematics. Question then became, what does all this mean?

So, back to Lorentz.

Along with a bunch of other natural philosophers (it is about this time that the term "physicist" started to replace that phrase), Lorentz was exploring the consequences and implications of Maxwell's equations. One of the things he was playing with was to see if he could find a way to make the laws of electromagnetism invariant in the same way that the laws of motion are invariant. What he discovered was that the introduction of the term "-c²t" made everything happy.

So, instead of just dealing with X, Y & Z, Lorentz discovered that we were really dealing with X, Y, Z and c²t. Mathematically speaking, this new time-based term behaves EXACTLY like the more familiar space-based terms and doing transformations between inertial frames of reference with electromagnetism was just like doing them with the motion of physical objects, only slightly more messy because you had to work with four dimensions instead of three.

Now, let's step forward another 15 years or so. Two young physicists named Einstein (remember I mentioned Albert's wife?) had an extraordinary year. In 1905, known as "Annus Miribilis", Einstein published four important papers.

The first showed that electromagnetism is not smooth "stuff" but is actually little bundles of energy which come in various discrete "sizes" (size is not really the right adjective because it suggests physicality but we'll leave that alone for now. This was an extension of the work by Max Planck but marked the introduction of the term "energy quanta." This paper also explained how light could be generated directly from flow of electrons (as opposed to just heating a wire until it is hot enough to glow) and that the reverse was also true -- electrons flowing because of electromagnetic waves. This is the paper which later earned Albert a Nobel Prize (the money for which he gave to his now-ex-wife).

The second paper was an explanation of Brownian motion -- the way particles in a fluid (either liquid or gas) jiggle and bounce around. The phenomenon was well documented and could be seen with a microscope but was not understood. This paper not only provided a mathematical model for this phenomenon but it also drove a stake in the idea of matter being smooth "stuff" and solidified (pun intended) the atomic model.

The third was special relativity. I'll come back to this one in a moment.

The fourth was on mass-energy equivalence. This paper showed that a particle has not only classical "potential energy" and "kinetic energy" but that the very concept of "mass" is an expression of energy, too. It is in this paper that the famous but rarely comprehended "E=mc²" equation is introduced.

But back to special relativity...

Galileo showed that motion is relative but didn't get the laws of motion right. Newton fixed that and gets credit for classical "Newtonian relativity" which works beautifully until things get to speeds approaching the speed of light. The Einsteins explained why (or, at least, offered a predictive, consistent and testable model which turned out to work very nicely. The reason it is called "special relativity" is because it is limited to a particular set of conditions, namely the same inertial frames of reference used by Newton. By applying the exact same Lorentz transformation (remember that "-c²t" fourth dimension Maxwell incorporated in his equations for electromagnetism?" to Newton's laws of motion, it was demonstrated that energy, mass, space (distance) and time are all interconnected AND showed that electromagnetism and the motion of physical objects are perfectly consistent with each other. At its core, special relativity says that everything is relative EXCEPT the speed of light. It is important to remark that special relativity is confined to inertial frames and to note that it necessarily neglects gravity. (Einstein would eliminate those two restrictions ten years later with "general relativity.")

I take the time to step through all this to demonstrate that "relativity" didn't just appear out of the blue (as seems to be a common misconception) but was a natural development springing from a couple hundred years of incremental advances by a bunch of really smart folks.

There are some peculiar implications of special relativity (and some even stranger ones from general relativity which contains all of special relativity plus much more, but we'll stay away from them for now...)

One that causes people headaches is that special relativity destroys the concept of simultaneity. That is, given any two events, A & B, separated by any distance, whether A happens before B, or B happens before A, or A and B happen at the exact same time it totally dependent on the observer's frame of reference. In fact, the concept of "at the exact same time" loses meaning because measuring time is a relative thing.

Another necessary implication of special relativity is length contraction. This says that, when an inertial frame of reference (and, by extension, an object being measured against that coordinate system) is moving, it gets "squished" along the direction of motion. The dimension of space literally contracts or gets compressed.

A fourth implication of special relativity is the equivalence of energy and mass. This one builds upon the E=mc² principle and it means that the apparent mass of an object depends on how fast it is moving. I say "apparent mass" not because it is an illusion but because mass is a relative thing, too -- how massive an object is depends on the relative motion between the object and the observer's inertial frame of reference.

A fifth implication (and this is the one you have been waiting for) is time dilation. If you take two identical clocks (the design and mechanics of the clock are irrelevant), synchronize them to the n^th degree, put one on a fast jet and fly it around the world, and then bring them back together again, you will find that the fast-moving clock slowed down. This is not a mechanical artifact of the design or construction of the clock and can be demonstrated in lots of other ways, too, but this "fly a clock around the world" approach has actually been tested. What special relativity predicts and requires, and what oodles of experiments have confirmed over and over, is that time literally gets "stretched out" or dilated. The amount to which it "slows down" is precisely described by Newton's laws of motion modified to include the Lorentz transformation and time gets slower and slower (or longer and longer, depending on how you want to look at it) depending on the relative speed between the observer and the object being observed. In fact, as the relative speed approaches that invariant "speed of light," the "length" of a time period (a "second" or "minute" or whatever you'd like to use) approaches infinity. Another way of stating that is to say the rate at which time ticks by gets slower and slower, until, as the speed approaches the speed of light, time grinds to a halt.

We say it takes eight minutes for light to travel from the Sun to the Earth (a distance of 93 million miles at a rate of 186k mph). If we could build a ship that rapidly accelerated to very, very nearly the speed of light and we sent it towards the Sun, an Earth-based observer would see it took just slightly over eight minutes to get there. For the passenger on the ship, however (assuming that person could somehow survive the acceleration), time would be ticking by so slowly that the trip would take practically no time at all -- the second hand on the observer's watch might not even move before the journey was over.

When you put the implications I list above together, it becomes apparent that we cannot accelerate an object to the speed of light. Mass goes to infinity and the rate at which you can develop a propulsive force goes to zero. We can approach the speed of light arbitrarily close, though, depending only on our technology. The clear implication, though, is that something somehow moving at the speed of light (like light itself, for instance) experienced no passage of time. In fact, time loses all meaning -- the "time" it takes for a photon to travel from the Sun to the Earth takes eight minutes from the perspective of someone on the Earth but it takes zero time from the perspective of the photon traveling at the speed of light. The "time" it would take for a photon to travel all the way across the universe (as we see it from Earth) would take zero time, too -- from the photon's perspective. At the speed of light, then, the "time" the photon would see on its wristwatch (if photons had wristwatches) at any point along that journey and beyond would be exactly the same. This is indistinguishable from the photon simultaneously being everywhere along that path.

Mind-boggling is right.

 

Thank you Brian for this brilliant introduction to Special Relativity. I am confident it will help some of us here to follow along when we are going to talk about some mind boggling questions now. Such as:

 

How come you at rest and I travelling in a space ship at relativistic speed will both measure the light of, let's say, a distant star to move 300'000 km/sec, even though what is a second to you is (for example) two seconds to me?

 

Another one: Why is c considered the highest possible speed in any frame if I in my relativistic space ship in fact travel at many times c, from my own view?