Speed of light is hard...

[The Great Sun Jester]

Ever since the speed of light became the universal speed limit, there has been the counter argument: if I'm taveling at almost the speed of light, and I turn on my flashlight do the photons emit at less than light speed? I know this argument is almost as viable as the airplane on the treamill one, but it escapes me why that's the case.

I guess my question is, is the speed limit relative to a starting point? or some other fixed point in space? or am I really not thinking about it in the right way?

[naita]

Ever since the speed of light became the universal speed limit, there has been the counter argument: if I'm taveling at almost the speed of light, and I turn on my flashlight do the photons emit at less than light speed? I know this argument is almost as viable as the airplane on the treamill one, but it escapes me why that's the case.

I guess my question is, is the speed limit relative to a starting point? or some other fixed point in space? or am I really not thinking about it in the right way?

The speed limit is the only absolute thing in a universe where everything else is relative. If you drive by me in your car at almost the speed of light, we'll both measure the photons your flash-light emits as moving at the speed of light. To me that will be because your time is slowed down by special relativity, to you that will be because you have an equal claim that I'm the one moving at almost the speed of light and that I'm the one whose clock is running slow.

Special relativity all the way!

[beowulff]

In your frame of reference, they appear to be traveling at “the speed of light” - 186,000 mi/sec. In a stationary frame of reference, they also appear to be traveling at the same speed. Which is why the speed of light is invariant (http://en.wikipedia.org/wiki/Invariant_speed).

[leahcim]

The point is that the statement, "if A sees B moving at velocity U, and B sees C moving at velocity V, then A sees C moving at velocity U + V", is true by every intuition we have, but nevertheless is wrong. In actuality, A sees C moving at (U + V)/(1 + U*V/c*c).

[Washoe]

Which is why the speed of light is invariant (http://en.wikipedia.org/wiki/Invariant_speed).

The invariance of the speed of light is a consequence of the postulates of special relativity, and the terms speed of light and invariant speed are often considered synonymous.

Bolding mine. I thought this was demonstrated by Maxwell’s equations. Wasn’t this established prior to the publication of Einstein’s paper? :confused:

[John Mace]

Ever since the speed of light became the universal speed limit, there has been the counter argument: if I'm taveling at almost the speed of light, and I turn on my flashlight do the photons emit at less than light speed? I know this argument is almost as viable as the airplane on the treamill one, but it escapes me why that's the case.

I guess my question is, is the speed limit relative to a starting point? or some other fixed point in space? or am I really not thinking about it in the right way?

It doesn't matter if you are traveling at .000000000001c or .9999999999999c. The speed of the photons will be c.

Think about it. If it* doesn't happen at low speeds, what would be the "magic" speed at which it suddenly started happening?

*"It" being the speed of the photon affected by the speed of the source.

[Candyman74]

Ever since the speed of light became the universal speed limit, there has been the counter argument: if I'm taveling at almost the speed of light, and I turn on my flashlight do the photons emit at less than light speed? I know this argument is almost as viable as the airplane on the treamill one, but it escapes me why that's the case.

It's not exactly a "counter argument" (it would require decades of experimental proof to gain that status, and there is none, given that it's not true).

It's a question, though, for sure, and a common one.

The answer is that - and this has been proven time and time again both mathematically and in practice for over a hundred years; there's no dispute that this is the case - the speed of light is the same for all observers whatever speed they're moving at. This is known as "relativity" and, yes, it's counter-intuitive, like much of our universe is. It "gets around" that by doing wacky things like actually slowing time down and stuff.

The speed of light is the same relative to all observers.

[tdn]

I still don't get it.

If Inigo is driving past me at nearly the speed of light, am I going to see his high beams all squished just in front of his car?

[YamatoTwinkie]

I still don't get it.

If Inigo is driving past me at nearly the speed of light, am I going to see his high beams all squished just in front of his car?

I believe the:

(1) High beams would be blueshifted considerably (you though HID headlights were annoying? How about X-ray headlights?),

(2) Inigo's entire car would be squished (in the direction of travel) quite a bit due to length contraction, from your perspective.

(3) From your perspective (at least for the fraction of a second it takes him to whiz by) Inigo will also appear to have time slowed down to a crawl.

[YamatoTwinkie]

whoops, nevermind about the X-ray thing. They'd still be blueshifted, but not to that degree.

[John Mace]

I still don't get it.

If Inigo is driving past me at nearly the speed of light, am I going to see his high beams all squished just in front of his car?

Yes, but the speed of propagation is independent of the wavelength.

[Leaffan]

I still don't get it either.

Explain it to a four year old.

[Punoqllads]

Time passes at different rates and distances are warped for observers moving with a nonzero velocity with respect to each other such that they both observe a given photon move at exactly the speed of light through a vacuum.

[Candyman74]

I still don't get it either.

Explain it to a four year old.

Can't. Relativity ain't an easy concept.

Some of the popular science books do a good job of it.

[John Mace]

I still don't get it either.

Explain it to a four year old.

What, exactly, don't you get?

[Leaffan]

What, exactly, don't you get?

So, I'm parked and light from my headlights is coming out of the bulbs at C.

Now I'm traveling at 100 KPH and light is still coming out of my headlights at C, because it can’t travel at C + 100 KPH.

Now I’m travelling at 0.5 C and light is still coming out at C.

Now I’m travelling at C, therefore no light can be emitted.

But I know that’s not correct.

Please correct what actually happens.

[beowulff]

So, I'm parked and light from my headlights is coming out of the bulbs at C.

Now I'm traveling at 100 KPH and light is still coming out of my headlights at C, because it can’t travel at C + 100 KPH.

Now I’m travelling at 0.5 C and light is still coming out at C.

Now I’m travelling at C, therefore no light can be emitted.

But I know that’s not correct.

Please correct what actually happens.

You can’t travel at C, but you can get arbitrarily close.

[John Mace]

So, I'm parked and light from my headlights is coming out of the bulbs at C.

Now I'm traveling at 100 KPH and light is still coming out of my headlights at C, because it can’t travel at C + 100 KPH.

Now I’m travelling at 0.5 C and light is still coming out at C.

Now I’m travelling at C, therefore no light can be emitted.

But I know that’s not correct.

Please correct what actually happens.

Everything is correct except the last part-- you can't travel at c unless you are light. Are you light? :)

[Tom Scud]

You can't actually get to C, because it would require an infinite amount of energy to accelerate you to C, and there isn't an infinite amount of energy. If you are at .99999999 C, you will still see your light traveling away from you at C.

[Musicat]

Some of the popular science books do a good job of it.

I recommend One, Two, Three, Infinity (http://www.amazon.com/One-Two-Three-Infinity-Speculations/dp/0486256642/ref=sr_1_1?s=books&ie=UTF8&qid=1322074521&sr=1-1) by George Gamow. Written 60 years ago, fun and easy to read. Explains relativity to a child (a pretty sophisticated child).

Hasn't lost its relevance, as long as the speed of light hasn't changed.

[Leaffan]

Everything is correct except the last part-- you can't travel at c unless you are light. Are you light? :)

No, in fact I've put on a few pounds.

[leahcim]

So, I'm parked and light from my headlights is coming out of the bulbs at C.

Now I'm traveling at 100 KPH and light is still coming out of my headlights at C, because it can’t travel at C + 100 KPH
.

A stationary observer sees the light emitted by your headlights travelling at c. Your 100kph observer would see the light moving at 100kph less than c, except that time is moving slower for it in exactly the right way so that the speed of the light with respect to the moving observer's time is also exactly c.

[John Mace]

A stationary observer sees the light emitted by your headlights travelling at c. Your 100kph observer would see the light moving at 100kph less than c, except that time is moving slower for it in exactly the right way so that the speed of the light with respect to the moving observer's time is also exactly c.

Not really. You sort of imply that the "stationary" reference frame is the correct one. Time only slows down in the moving reference frame when observed from the stationary one. Either reference frame could be considered "stationary", with the other one moving.

[Punoqllads]

So, I'm parked and light from my headlights is coming out of the bulbs at C.

Now I'm traveling at 100 KPH and light is still coming out of my headlights at C, because it can’t travel at C + 100 KPH.

Now I’m travelling at 0.5 C and light is still coming out at C.

Now I’m travelling at C, therefore no light can be emitted.

But I know that’s not correct.

Please correct what actually happens.
One of the things about relativity is that "traveling" is not an inherent property of something, only traveling relative to a given observer. Hence, relativity. So one observer sees you moving at velocity 0.5 c and you, by symmetry observe that observer moving at velocity of -0.5 c -- that is to say, 0.5 c in the opposite direction. Your headlight then emits a photon in the direction you're traveling. After 1 second has passed, you see that it has traveled exactly one light-second (approximately 300,000,000 meters).

But time and distance are relative to an observer. You observe one second pass, but when you mark that point in time t and the distance the photon traveled x, the observer has seen t' seconds pass, where t' = gamma * (t - v * x / c2) where v is your velocity = 0.5 c, and they've seen the photon move distance x', where x' = gamma * (x - v * t). In both formulas there is a factor called gamma = 1 / sqrt(1 - v2 / c2). These equations are called Lorentz transformations (http://en.wikipedia.org/wiki/Lorentz_transformation) and gamma is called the Lorentz factor (http://en.wikipedia.org/wiki/Lorentz_factor).

[The Great Sun Jester]

As far as the time thing changing from an observer's perspective, I think this was fairly well-explained in Young Einstein. He muses about what a clock face would do (from your perspective) if you were traveling away from it. Light bounces off the clock face and into your eye at the speed of light. But when you're moving away from it, it takes longer for those photons to reach your eye the closer your speed approaches that of light. When you reach the speed of light, the clock will appear to have stopped. From this I have to ask two things:

1) wouldn't the clock face also seem to dim? After all, there is only one set of photons bouncing off of it at any given moment, once those hit your eye, there are no more if you're traveling away from them at the same speed they're moving toward you.

2) If you approach something at the speed of light, would time (at the target) appear to speed up from the perspective of the traveler?

[Musicat]

Just my 2 cents worth...while it seems counter-intuitive that the beams of light from passing cars would travel at the same speed when the generating vehicles are converging or diverging at high speeds, it is a necessary consequence of our observations. If light is not constant from/to all observers, we have an awful lot of 'splainin to do, Lucy.

Perhaps it's a bit like the Ptolemaic solar system, (http://en.wikipedia.org/wiki/Geocentric_model) which, using epicycles upon epicycles, was able to (almost) compute planetary positions accurately. The Copernican system (http://en.wikipedia.org/wiki/Copernican_heliocentrism) removed the need for the complicated compensations by simply adjusting the frame of reference.

I see a parallel here to relativity, which simply explained a number of failures and observations, like the Michelson-Morley Ether (http://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment) experiments. The speed of light may not be constant, but assuming that it is sure answers a lot of questions, explains a lot of otherwise puzzling stuff, and is the best computational system we have found so far.

[RealityChuck]

Bolding mine. I thought this was demonstrated by Maxwell’s equations. Wasn’t this established prior to the publication of Einstein’s paper? :confused:I think you mean the Lorentz Transformation Equations, which do predate Einstein. Lorenz was commenting on the Michaelson-Morley Experiment, which showed that the speed of light was a constant. No one understood the results; Lorenz came up with equations that would have explained it, but it was only an intellectual exercise which left scientists saying, "well, yes, but why would they work that way?"

Einstein explained why and thus Lorenz's equations became more than an exercise.

[Chronos]

Bolding mine. I thought this was demonstrated by Maxwell’s equations. Wasn’t this established prior to the publication of Einstein’s paper?Yes and no. Maxwell's equations yield a single unambiguous value for the Speed of Light, but are completely mute on the question of what this speed is relative to. Before Michelson and Morley, the prevailing consensus was that there was some substance called the "ether" which pervaded the Universe, and that the speed of light was relative to the ether. Einstein, however, interpreted it differently: The speed of light is relative to everything, all at once, with no ether necessary.

Oh, and RealityChuck, Lorentz and Lorenz were, confusingly, two completely different turn-of-the-century physicists, who occasionally even worked together. There's actually something called the Lorentz-Lorenz Effect which is named after both of them. The one you meant to be referring to throughout that post was the one with the T.

[Keeve]

So, I'm parked and light from my headlights is coming out of the bulbs at C.

Now I'm traveling at 100 KPH and light is still coming out of my headlights at C, because it can’t travel at C + 100 KPH.This is exactly correct. But I'll fill in some missing pieces:

I'm standing outside your car. From my point of view, I see you moving at 100 KPH, and I see the photons of your headlights moving at C. I do some mental math, and I laugh, and I say, "He thinks his car is giving an extra push to those photons, and that they're going at a speed of C + 100 KPH! But that's impossible! They're still going only C relative to me, and they're going C minus 100 KPH relative to him!"

But that's not accurate. Relative to you, they really are going at C. That's because time and space have adjusted slightly. Time is slowing down for you - relative to me. Therefore, even though I think the photons should appear to you as moving slightly slower than usual, your own slowed time compensates for that, and the result is that the photons appear totally normal to you.

Now, suppose you say, "NO! I know my car is moving at 100 KPH, so what you're saying doesn't make sense." But you're not allowed to say that, because it constitutes cheating. It is cheating, because when you say "my car is moving at 100 KPH", you are saying that from MY point of view. You can't have it both ways. "Relativity" always means "Relative to what?", and you can't change the rules in the middle of the game.

[The Hamster King]

Light bounces off the clock face and into your eye at the speed of light. But when you're moving away from it, it takes longer for those photons to reach your eye the closer your speed approaches that of light. When you reach the speed of light, the clock will appear to have stopped.


No. Propagation delay is not the mechanism that causes time dilation. Because if it were (as you correctly conclude) clocks should run faster if we're approaching them.

Here's the easiest way I've found to understand it:

EVERYTHING moves at the speed of light ALL THE TIME through 4-dimensional space-time. When something appears to be stationary, it's because all of its motion is in the time dimension, and none of it is in any of the three space directions.

When something appears to be moving, it's because some of its motion is in a spatial dimension. But since it's always traveling the same speed in 4-D space-time, any increase in motion in space reduces it motion in time -- i. e. clocks run slower for moving objects.

However (and this is the big point) what constitutes a "time dimension" and what constitutes a "space dimension" varies from observer to observer. From my perspective, I'm stationary and moving through time normally. You're moving through space, so you're moving through time more slowly. But from your perspective, you're stationary and moving through time normally, while I'm the one who's moving through time more slowly.

The direction of the time axis through 4-D space-time varies from observer to observer. It's not that clocks slow down for moving things. It's that when two observers are moving relative to each other, they perceive the arrow of time as pointing in different directions.

[Askance]

Relativity in 5 minutes (http://www.youtube.com/watch?v=KYWM2oZgi4E) on Youtube.

[Andy L]

Yes and no. Maxwell's equations yield a single unambiguous value for the Speed of Light, but are completely mute on the question of what this speed is relative to. Before Michelson and Morley, the prevailing consensus was that there was some substance called the "ether" which pervaded the Universe, and that the speed of light was relative to the ether. Einstein, however, interpreted it differently: The speed of light is relative to everything, all at once, with no ether necessary..

Although, if you attempt to combine Maxwell's equation with the idea implicit in Galilean relativity that the laws of physics ought to be invariant with constant motion, you arrive at relativity, so in that sense, Maxwell's equations implied relativity.

[Nametag]

Everything is correct except the last part-- you can't travel at c unless you are light. Are you light? :)
He ain't light, but he ain't heavy.
He's my brother

[Chronos]

Although, if you attempt to combine Maxwell's equation with the idea implicit in Galilean relativity that the laws of physics ought to be invariant with constant motion, you arrive at relativity, so in that sense, Maxwell's equations implied relativity. Yes, though this is clearly not as obvious as it seems to us, given that it took Einstein to realize it.

[The Great Sun Jester]

EVERYTHING moves at the speed of light ALL THE TIME through 4-dimensional space-time. When something appears to be stationary, it's because all of its motion is in the time dimension, and none of it is in any of the three space directions.

When something appears to be moving, it's because some of its motion is in a spatial dimension. But since it's always traveling the same speed in 4-D space-time, any increase in motion in space reduces it motion in time -- i. e. clocks run slower for moving objects.This hurts. So basically I can't think about very fast motion without also thinking about time? Am I getting hung up because I think of thing in Newtonian terms where stuff can always go a little faster and weigh a little more with no practical upper limit?

Would it be more appropriate to think of the universe as having a resistance to motion akin to water? Cuz when you move through water, you get little resistance at low velocity and can do pretty much what you want, but higher velocities require you to overcome the resistance/inertia of the water that's in your way. At some point it seems there would be a maximum speed at which you simply can't overcome it because the density of the water directly in front of you exceeds your own and you start to flatten against it. I'm sure that's the wrong way to think about high speeds in the near vacuum of space, but how wrong is it?

[naita]

Would it be more appropriate to think of the universe as having a resistance to motion akin to water? Cuz when you move through water, you get little resistance at low velocity and can do pretty much what you want, but higher velocities require you to overcome the resistance/inertia of the water that's in your way. At some point it seems there would be a maximum speed at which you simply can't overcome it because the density of the water directly in front of you exceeds your own and you start to flatten against it. I'm sure that's the wrong way to think about high speeds in the near vacuum of space, but how wrong is it?

Very wrong. You've almost stumbled back into Aristotelian physics where continued motion requires continued force, and you're also close to the concept of an ether.

What you need to grasp first is that there is no such thing as high speeds, except in relation to other objects. And no objects are more equal than others.

[Alka Seltzer]

Oh, and RealityChuck, Lorentz and Lorenz were, confusingly, two completely different turn-of-the-century physicists, who occasionally even worked together.

So, which one is the anti-particle?

[Bryan Ekers]

Are you light? :)

Well, he won't be after Thanksgiving.

[OpalCat]

It's hard for me to understand as well. I have this additional question: if I turn on a light, it is automatically traveling at the speed of light, regardless of how much energy went into the light being created, right? So it wouldn't take any more or less energy to make light travel at the speed of light if I'm standing still (relative to whatever reference point) vs. traveling at .9999 the speed of light. How is it that it takes the same energy to make something accelerate to the speed of light from 0 as opposed to .9999 c?

[Candyman74]

It's hard for me to understand as well. I have this additional question: if I turn on a light, it is automatically traveling at the speed of light, regardless of how much energy went into the light being created, right? So it wouldn't take any more or less energy to make light travel at the speed of light if I'm standing still (relative to whatever reference point) vs. traveling at .9999 the speed of light. How is it that it takes the same energy to make something accelerate to the speed of light from 0 as opposed to .9999 c?

I don't know the answer to this question, but I'll make a guess: light has zero mass. Anything multiplied by zero is zero. Or something.

[Chronos]

Photon energies do vary; they just don't vary based on velocity. If you're moving forward at high speed in some reference frame, and turn on your headlights, the photons from your headlights will, in fact, be higher energy (in that frame) than if you were standing still.

[Andy L]

Yes, though this is clearly not as obvious as it seems to us, given that it took Einstein to realize it.

Absolutely!

[Lemur866]

It does add energy to the light. If you're traveling at .99c and turn on the headlights, the light gets more energy. One way it could get more energy is to be traveling faster. But it can't do that. So instead the light gets a higher frequency. It gets blue-shifted. And the opposite happens. As you're traveling .99c and turn on the taillights, the taillights lose energy and get redshifted.

And so, objects traveling towards you will be blueshifted, objects traveling away will be redshifted. And when we observe distant galaxies they are all redshifted, which means they are all traveling away from us, which means in the past they were closer together, which leads back to the Big Bang.

[OpalCat]

But how does the light "know" that it should be higher energy, lower velocity?

See this is why I didn't go into the sciences in college....

[Lemur866]

It knows it has higher energy for the same reason the baseball you throw from your moving car knows it has higher energy. It has higher energy because, as per your intuition, the energy added to the light from your .99c traveling spaceship can't just disappear.

So, the kinetic energy of an object is mv^2/2, or mass, multiplied by velocity squared, divided by two. So when you have a ball weighing one kilogram and throw it at 10 meter/second you have a certain amount of kinetic energy. Throw it at the same speed from a car moving 10 meters/second, and it's moving at 20 meters/second, and so it has more kinetic energy. Throw it backwards at 10 meters/second, and you find that it is moving at 0 meters/second, and has zero kinetic energy.

Same thing with the light, except you can't make the light travel faster. So what happens instead is that the equivalent of the mass of the ball increases--in this case, the energy of the photon. So radio waves increase in energy to microwaves, microwaves increase to infra-red, red to yellow, yellow to blue, blue to ultraviolet, ultraviolet to x-rays, x-rays to gamma rays. All these photons travel at the same speed, but have higher and higher energies.

[The Hamster King]

\And when we observe distant galaxies they are all redshifted, which means they are all traveling away from us, which means in the past they were closer together, which leads back to the Big Bang.A quibble:

When galaxies move toward or away from us, their light is blue-shifted or red-shifted. However, the red shift we see for very distant galaxies is NOT caused by their relative velocity away from us. It's caused by the expansion of space over the billions of years the light took to reach us. Essentially the light wave has been slowly stretched over the duration of its trip.