What's so special about C?

[SkepticalScience]

So what makes the speed of light such a special constant in the universe?

Why can't we travel faster than light, without resorting to some “trick� like using wormholes or the like?

What is it that actually prevents clever engineers from developing an engine that can break the light barrier, just as engineers broke the sound barrier previously.

I have a feeling that it has something to do with things getting “massier� as more energy is applied to them – but what makes 186,000 mps so special??

Can someone help a skeptic out by explaining this madness in laymens terms!

THANKS!
SS

[rppa]

You probably won't like the answer but: It's not that light sets a speed limit. It's that the universe sets a speed limit. Light goes as fast as the universe allows it to, which is c. But c is a property literally of the fabric of space and time.

Why is it the number it is? The hope for a Theory of Everything is that eventually instead of a bunch of different constants of the universe (c is not the only one) we'll have one theory that explains all of them. But till then, the best we can do is say, here are the constants that have been handed to us.

[Johnny Pneumatic]

It is indeed due to mass. The reason is as you get up to relatavistic speeds the mass of an object gets greater and thus takes more energy to make it go even faster, and so on. At the speed of light itself the mass of any object is infinite. It would take an infinite amount of energy to push something with infinite mass so that's why it's impossible. Someday we might be able to get up to 0.9 or more C, maybe; but never 1.0.

[Terry]

Well, it's high enough level to be somewhat portable, but close enough to the machine to do system programming.

Oh, not the programming language? never mind...


--Terry.

[Dilb]

The only "special" thing about c is that oberservations have been made that c is constant in any reference frame. This (single) observation then leads to a lot of different things, ie all of relativity. The fact that physicists

1. Assumed c to be constant
2. Derived theories that would have to be true for c to be constant
3. Observed these new theories to be correct

make it very justifiable that c is constant. But it's entirely possible to imagine a universe where this isn't true, it just isn't correct to do so. Any space computer game will use Newtonian mechanics (or even simpler ones, maybe), since it's not really possible or necessary to use relatavistic calculations.

To expand on this:
It is possible to go faster than light, infact this leads to an interesting type of radiation, Cerenkov radiation, explained here (http://www.straightdope.com/classics/a990430a.html). You can't go faster than the speed of light in a vacuum. Although I think even with this radiation you're only exceeding the bulk/average speed of light in a medium.

2 Sound is determined by the elasticity of a material, so by having more than one type of material and making a sound, you've already got something (a different sound, admittedly) moving faster than sound. Also, simple experiments will show that the speed of sound is not constant for reference frames, this is the doppler effect, so it's a just a matter of moving faster and seeing sound move slower relative to you. Go fast enough and you beat sound.

Essentially, there's no better answer than "light is always moving at lightspeed relative to you, regardless of how fast you move, as confirmed by experimental results". It's simply how the universe works. From the cockpit of your super-hyperpowered-spaceship, light is always constantly outrunning you, regardless of your speed or acceleration.

[Tez]

Originally posted by Dilb
The only "special" thing about c is that oberservations have been made that c is constant in any reference frame. This (single) observation then leads to a lot of different things, ie all of relativity. The fact that physicists

1. Assumed c to be constant
2. Derived theories that would have to be true for c to be constant
3. Observed these new theories to be correct

make it very justifiable that c is constant. But it's entirely possible to imagine a universe where this isn't true, it just isn't correct to do so. Any space computer game will use Newtonian mechanics (or even simpler ones, maybe), since it's not really possible or necessary to use relatavistic calculations.

To expand on this:
It is possible to go faster than light, infact this leads to an interesting type of radiation, Cerenkov radiation, explained here (http://www.straightdope.com/classics/a990430a.html). You can't go faster than the speed of light in a vacuum. Although I think even with this radiation you're only exceeding the bulk/average speed of light in a medium.

2 Sound is determined by the elasticity of a material, so by having more than one type of material and making a sound, you've already got something (a different sound, admittedly) moving faster than sound. Also, simple experiments will show that the speed of sound is not constant for reference frames, this is the doppler effect, so it's a just a matter of moving faster and seeing sound move slower relative to you. Go fast enough and you beat sound.

Essentially, there's no better answer than "light is always moving at lightspeed relative to you, regardless of how fast you move, as confirmed by experimental results". It's simply how the universe works. From the cockpit of your super-hyperpowered-spaceship, light is always constantly outrunning you, regardless of your speed or acceleration.

Be careful not to confuse speed and frequency re the doppler effect Dilb.

SkepticalScience, here is something I have always found amazing. Consider a collection of massive particles on the vertices of a square lattice, coupled by springs to their nearest neighbours. Think of this as a "mattress". You can imagine "waves" travelling through the mattress - if you bounce at one point, the oscillations will fan out from there.

Now if you consider the waves which have a long wavelength - i.e. distance between peaks and troughs - (equivalent to a low oscillation frequency), and in particular the waves which have a wavelength that is long compared with the distance between the particles, then you find the following remarkable thing: All inertial observers of these waves will see them travel with a constant velocity - lets call it c. In modern language, the description of these waves is Lorentz invariant.

Why is this amazing? Because we start off with a description that is NOT Lorentz invaraint - we start off with a bunch off massive particles, embedded in some kind of Newtonian spacetime. That is, the underlying theory of our massive particles and springs is a theory in which the standard "sensible" Newtonian/Galilean transformations of space and time coordinates hold.

In effect, many people think that this picture does describe what happens with light in our universe - they believe that at a small enough scale (known as the Planck scale) we will see the "discreteness" of the mattress. Such discreteness could manifest itself in the propogation properties of light that has a short wavelength (high energy/high frequency) - in particular, this light may travel with a velocity that doesnt quite match c. In fact, there are already people trying to observe this in high energy photons that have travelled cosmological distances...

[69dodge]

Originally posted by Tez
Now if you consider the waves which have a long wavelength [ .. ] then you find the following remarkable thing: All inertial observers of these waves will see them travel with a constant velocity?!

I am missing something here ...

[Tez]

Originally posted by 69dodge
?!

I am missing something here ...

You'll have to be more specific - you dont understand why, or you dont understand what!

[Dylab]

I don't understand the why. Can you elaborate. Why is it invariant?

[69dodge]

I think I understand what you said, but I also think I disagree with it. So, probably I don't actually understand it.

Are the waves transverse or longitudinal? How exactly are we defining "wave velocity"? Are we talking about the phase velocity of a single frequency or the group velocity of a wave packet?

Not sure why any of this should matter; I'm just trying to get a definite picture in my head.

Since spacetime is Galilean, nothing prevents one observer from moving at "c" relative to another. Then what? One observer sees the other keeping pace with a wave, while the other sees the wave passing himself at "c"?

I don't get it at all.

[Dilb]

Originally posted by Tez
Be careful not to confuse speed and frequency re the doppler effect Dilb.


Oops, right. That should be more like "the relative velocity of sound changes, so it takes longer for a sound to reach you if you're moving away, compared to a stationary person, when you start at the same position." It could be measured with the doppler effect, but the same applies to light, despite it's relative velocity not changing.

[IIRichard]

I personally find Pi more interesting. Could you have a universe where Pi doesn't = 3.14159 . . . . . .? Or is an irrational number like the square root of two?
______________________________
edi9ted to correct stupid speeeling masteak

[neutrino_cannon]

The sound and light barriers are different beasts. Well before the X-1 eve got slung off of its B-29 mothership, hot 30-06 loads had been exceeding the speed of sound since 1906, as the name would suggest. Flinging something through a medium at a velocity greater than that medium's rate of transmission of certain waves doesn't necessarily violate any physical laws, though it usually has some nifty and/or strange effects (google for "Cherenkov Radiation").

All that stood in the way of supersonic flight in the 1940's was the lack of mature jet engines with afterburners and a complete understanding of some of the aerodynamic strangeness that happens when flying past the speed of sound. Those may not have even been such a huge problem, numerous anecdotal reports suggest that diving f-86's could and did break the sound barrier in Korea. Years of experience with bullets showed engineers that breaking the sound barrier was just a matter of brute force and streamlining.

By contrast, flinging something with at the speed of light appears impossible because the amount of energy required keeps going up and up until it requires an infinte amount of energy to propell something with mass at c. Particle accelerators have this problem. Google something called the "oh my god particle". Basically it's a proton with the kinetic energy of a baseball, owing to it's moving at a fly's eyelash below c. Yes, that's a single proton with enough punch to knock over your neighbor's cocker spaniel, all because of the goofiness of Einsteinian physics. Throwing more and more energy in gives increasingly reducing returns in projectile velocity, which suggests that something mighty powerful indeed it producing the "oh my god" particles. Unlike the sound barrier, there is no prior human invention that can break c, and there is no clear means by which to do so.

[espritch]

I personally find Pi more interesting. Could you have a universe where Pi doesn't = 3.14159 . . . . . .?

From what I understand, we already live in a universe where Pi doesn't neccessarily equal 3.14159... Gravity warps space. If you measure a direct radial line from the center of the earth to a point in space and then measure the circumference of a circle around the earth that passes through that point, you will find that the lenght of the circumference does not actually equal Pi times the radius; it is a little less due to the warping of space by Earth's gravity well. So if Pi is defined as the relationship between the radius of a circle and it's circumference, it will only be 3.14159... in a perfectly flat region of space time, which, as far as I know, doesn't actually exist.

[neutrino_cannon]

c.f. Terry Pratchet's recent book Going Postal, in which a wheel where pi=3 is a very dangerous thing indeed.

[Tez]

You don't need to "believe me" or otherwise - anyone who knows enough to be skeptical, probably knows enough to do the derivation themselves! Its fairly standard.

(That said, I had to google for 15-20 minutes to find a coherent but also rigorous discussion to link to!)

See e.g. Stetz' book:

http://www.physics.orst.edu/~stetza/COURSES/ph655/Book.pdf

The relevant part is chapter 4, pages 33-39. Note, I dont claim you must agree with the conclusions he draws, but the analysis is fine.

Someone asked the good question of why, if the background spacetime is Galilean, could one not have observers travelling faster than c. If you trust regularized quantum field theory (which is all this stuff actually is) then its for the simple reason that the "observers" are made out of the same junk! That is, from this perspective, we are all made up of the oscillations of a slightly more complicated version of the "masses and springs" mattress, (but not much more complicated!) and are similarly limited in our maximum velocity (in fact, being massive excitations, our dispersion relation is such that we cannot quite reach c).

Which brings me to the issues I have with this point of view. It seems the background spacetime retreats into a metaphysical structure if you adopt this approach. That I'm a little worried about, but there's enough historical precedent for such, and I am not rooted in postivistic philosophy; my epistemology will survive. However certain technical questions arise as to how, why or even if the theory is such that classical reference frame objects (clocks, metre sticks) can be built from the "oscillations" (excitations of the field), and these questions disturb me. For instance, if you read those pages above, the final wave equation contains a parameter "t" corresponding to time. This parameter originally arose from the background galilean spacetime. However, it must now be measured with clocks that are built from the field itself. If you try and make rigorous these constructions you find that there is no simple operational interpretation of this time. And yet we use this wave equation very successfully all the "time"! There are several proposals by leading physicists for how to give a consistent interpretation of time in such a scenario, but none of them have completely satisfied me...

[69dodge]

Ok, I read your link. Also, p.180 of http://www.ifa.hawaii.edu/~kaiser/lectures/elements.pdf. It seems you weren't saying what I thought you were saying.

Which is what I figured. :D

Tell me if have it right, now.Originally posted by Tez
All inertial observers of these waves will see them travel with a constant velocity - lets call it c.Yes, if those inertial observers are related to the mattress frame (no pun intended) via Lorentz transformations. (I originally thought these transformations were supposed to be Galilean too, just like the laws governing the oscillations of the mattress.) But then, it's no surprise that an observer still sees the wave travelling at c; that's built into the Lorentz transformation. The only interesting thing is that the transformed wave, in all its details, is (a different) one of the possible original waves.In modern language, the description of these waves is Lorentz invariant.Right. So if different inertial observers are related via Lorentz transformations, then they can all use the same description to describe the waves. But we can't derive the fact that they are related via Lorentz transformations unless we assume that they can all use the same description.

[Tez]

Originally posted by 69dodge
Ok, I read your link. Also, p.180 of http://www.ifa.hawaii.edu/~kaiser/lectures/elements.pdf. It seems you weren't saying what I thought you were saying.

Which is what I figured. :D

Tell me if have it right, now.Yes, if those inertial observers are related to the mattress frame (no pun intended) via Lorentz transformations. (I originally thought these transformations were supposed to be Galilean too, just like the laws governing the oscillations of the mattress.) But then, it's no surprise that an observer still sees the wave travelling at c; that's built into the Lorentz transformation. The only interesting thing is that the transformed wave, in all its details, is (a different) one of the possible original waves.Right. So if different inertial observers are related via Lorentz transformations, then they can all use the same description to describe the waves. But we can't derive the fact that they are related via Lorentz transformations unless we assume that they can all use the same description.

I think you've got it. I guess in principle we can imagine what things are like if you don't happen to be "in the mattress frame" (which is probably better thought of as "made of the mattress"). For instance, this is a reasonable enough model of long wavelength phonon propogation, and we can certainly imagine sitting outside the crystal and bopping along at any old veocity we want. I'd have to think about what this meant for a coherent description of physics from this observers viewpoint. I suppose they essentially end up in a messy situation much like people were in when they realized Maxwell's equations didnt transform under a Galilean transofrmation, but regular matter (supposedly) did...

[Dustin Kesselberg]

I have a few questions which do not seem to have been answered even though this thread pertains to them...


1.How did einstein know the speed of light?


2.Why did he assume that it was always constant?


3.How did he know it was always constant?


4.Why is mass infinite at the speed of light?


5.How did einstein know mass is infinite at the speed of light?

[Darat]

Originally posted by Dustin
I have a few questions which do not seem to have been answered even though this thread pertains to them...


1.How did einstein know the speed of light?


When?

Originally posted by Dustin


2.Why did he assume that it was always constant?


His genius.

Originally posted by Dustin


3.How did he know it was always constant?

...snip...



When?

Originally posted by Dustin


5.How did einstein know mass is infinite at the speed of light?

He didn't.

[Dustin Kesselberg]

Originally posted by Darat
When?



His genius.



When?



He didn't.


1.When he said it was constant.

2.That's not an answer.

3.When he said it was always constant.

5.No?Who did?

[Darat]

Originally posted by Dustin
1.When he said it was constant.


But he said it at different times of his life, and at during his lifetime many measurements were made, do you mean when he first came up with his theories?

Originally posted by Dustin

2.That's not an answer.


Sorry not only is it an answer it's also the correct answer! His genius was that he thought about a new way to perhaps describe, via mathematics, the world, subsequently his theories became testable and it was found out that his maths does seem to pretty much describe how the world "works". However we also now know (from other observations of the world) that his theories are not a complete description of the world.

Originally posted by Dustin


3.When he said it was always constant.


He didn't know.


Originally posted by Dustin


5.No?Who did?

No-one. Remember these are theories, not a form of religious truth so its all about remembering that when someone says they “know� they are probably meaning something more like “all the observations we have confirm this part of his theory so we can say we know it to be true� but that doesn’t mean it is true.

[Dustin Kesselberg]

1.When Einstein First came up with his theories he based them on the speed of light.

2.Assuming something is always constant when it has never even been measured makes no sense.

3.So what you are telling me is that Einstein did not know the speed of light was constant but assumed it was constant?This also makes no sense.

5.In experaments,it has been observed that when speeding a particle to the speeds of light..It does not pass the speed of light. It's mass increases while it's speed does not.

[Darat]

Originally posted by Dustin
1.When Einstein First came up with his theories he based them on the speed of light.


No, that's not quite correct the idea that the speed of light is a constant is part of his theory. I don't know the history of his development of his various theories well enough to provide you with when he first started using that idea.

Originally posted by Dustin

2.Assuming something is always constant when it has never even been measured makes no sense.


Quite right, that's why he was a genius! Remember many people considered the idea "crazy" at the time, even ones who could speak the same language! If those people had been able to show his maths was wrong or the theories had been found not to (accurately) describe the observable world Einstein would just be an obscure footnote in the long history of scientists who came up with theories that didn't "work".


Originally posted by Dustin

3.So what you are telling me is that Einstein did not know the speed of light was constant but assumed it was constant?This also makes no sense.


And I daresay that is why he is today considered a genius and you and I aren't! :)

Originally posted by Dustin

5.In experaments,it has been observed that when speeding a particle to the speeds of light..It does not pass the speed of light. It's mass increases while it's speed does not.

?

[Dustin Kesselberg]

2.Being "genius" does not mean you are illogical,Or Psychic. Einstein must of had a way of knowing the things he claimed otherwise he was just good at guessing.

3.See No.2

5.Nevermind.

[Darat]

Originally posted by Dustin
2.Being "genius" does not mean you are illogical,Or Psychic. Einstein must of had a way of knowing the things he claimed otherwise he was just good at guessing.

...snip...


He did have a way in that he created a theory that was consistent (mathematically speaking), however he made assumptions in that theory, probably the now most famous is his "cosmological constant" that he described as his greatest "blunder". In other words he "fiddled" his equations because at the time he thought without the constant they didn’t actually describe the universe as he understood it.

I think you are missing out why Einstein is today still considered such a genius, it was the fact that he thought (at the time) like no one else had ever done before and had the sheer intelligence and mathematical ability to turn that new way of thinking into a coherent theory.

[Roboramma]

Originally posted by Dustin
I have a few questions which do not seem to have been answered even though this thread pertains to them...


1.How did einstein know the speed of light?

It was experimentally tested.

Originally posted by Dustin

2.Why did he assume that it was always constant?

The Michelson/Morely experiment showed that there was no mesureable differance between the speed of light from the sun as the rotation of the earth carried the experimenter toward the source of the light, and when moving away from it.
At least, that's how I remember the experiment... someone else might correct me if I've got the details wrong, this is only high school physics I'm recalling.
Anyway, from that experiment it seemed that the speed of light was constant regardless of the observer moving toward or away from it.

As for your other questions, I don't know enough to comment intelligently. ;)

[Dustin Kesselberg]

Originally posted by Roboramma
It was experimentally tested.


The Michelson/Morely experiment showed that there was no mesureable differance between the speed of light from the sun as the rotation of the earth carried the experimenter toward the source of the light, and when moving away from it.
At least, that's how I remember the experiment... someone else might correct me if I've got the details wrong, this is only high school physics I'm recalling.
Anyway, from that experiment it seemed that the speed of light was constant regardless of the observer moving toward or away from it.

As for your other questions, I don't know enough to comment intelligently. ;)

It was tested 80 years ago?

[Roboramma]

Originally posted by Dustin

5.In experaments,it has been observed that when speeding a particle to the speeds of light..It does not pass the speed of light. It's mass increases while it's speed does not.

Almost.. as the speed of the particle increases, it's mass increases exponentially(or something like it). It's a curve that goes up and up as the speed increases, but will only reach the speed of light at infinity.
The fact that mass increases as velocity increases is easy to see from:
1. E=m c squared (how do I use superscript?)
2. E increases as v increases.
if E increases and c is constant, m must increase as well.

Well, that doesn't tell you how much m increases, but E = mc(c) is only one simple equation in the theory, and there are other parts of the math that would show the exact relationship.
Again, I don't really know enough about it to comment, though...

[Darat]

Originally posted by Dustin
It was tested 80 years ago?

I think the first person to give a value for the speed of light was Roemer back in the 17th century.

(Edited to add.)

There is a very good website (IMO) for the The Michelson-Morley Experiment see http://galileoandeinstein.physics.virginia.edu/lectures/michelson.html

[Roboramma]

Originally posted by Dustin
It was tested 80 years ago?

I think it was more than that. Actually, I thought it was at the end of the nineteenth century, but again, I could be wrong about the exact date.
I'm not exactly sure how it was done, but they used rotating mirrors, and based on how far a mirror moved before light from another mirror struck it, they could determine the speed.
Well, something like that anyway. I'm in an internet cafe in bangkok right now, and they connection isn't the greatest for looking these things up. :)

[drkitten]

Originally posted by Dustin
It was tested 80 years ago?

More like 120. The results of the famous Michaelson-Morley experiment were published in 1887, and showed that the speed of light did not vary with the earth's direction of travel through the hypothesized ether -- or in other words, that the speed of light appeared to be constant irrespective of the motion of the observer.

By 1903, when Einstein published the Theory of Special Relativity, this experiment and its findings were well-known.

There's a brief discusson on Answers.com (http://www.answers.com/topic/michelson-morley-experiment) if you want more information.

[NarrMaster]

I believe (I think I read this in "Einstein's Universe") that Einstein attempted to concieve of a wave of light travelling at less than light speed, and came to the conclusion that it was a contradiction. Part of the "thought experiment" included travelling at "C" with the beam of light, and measuring it. A beam of light that is stationary relative to an object is meaningless, apparently.

Just thought I'd throw that out there.

[Pragmatist]

Originally posted by Dustin
I have a few questions which do not seem to have been answered even though this thread pertains to them...


1.How did einstein know the speed of light?


2.Why did he assume that it was always constant?


3.How did he know it was always constant?


4.Why is mass infinite at the speed of light?


5.How did einstein know mass is infinite at the speed of light?

1. Einstein knew the speed of light because it had been measured many times. I have a paper of Maxwell's that predates Einstein by about 50 years in which he mentions various different measurements of the speed of light.

2. Because no matter how they did measurements of it, regardless of whether the apparatus was standing still or moving, the measurement always seemed to come out the same (within the limits of experimental error). In particular, interference type measurements, would have shown a noticeable phase shift when the apparatus was in motion if the speed of light was not a constant - they didn't.

3. Already answered in 2. He didn't know it absolutely, but all the experimental evidence available at the time seemed to indicate that it was.

4. Because once you accept that the speed of light is constant for all observers it changes the fundamental geometry of the universe itself. Space is no longer Euclidean at high speeds but rather Minkowskian. In order to maintain observed physical laws and in particular to maintain conservation laws, when one thing changes, other things have to change. The 3 fundamental properties recognised in physics are mass, length and time. Setting the speed of light as a constant causes changes in time. Therefore there have to be corresponding changes in length and mass as well, otherwise all our physical laws and conservation goes out the window. The result of adjusting time to suit the observed effects results in length apparently contracting at high speeds and mass increasing. The limit of all such effects is the speed of light itself. Time goes to zero, length goes to zero and mass becomes infinite.

[IIRichard]

I believe Gallileo made a rough determination of the speed of light by timing the re-appearance of the moons of Jupiter. When Jupiter was farther away from the earth, the eclipse and reappearance took longer. He correctly believed it was due to the fact that light had a finite speed.

Over the years, the value was calculated more precisely.
James Clerk Maxwell formulated equations of electromagnetics that predicted the known value.

Michaelson measured the speed of light to great precision. He also wanted to show that the assumed medium for the propagation of light, the aether, existed. He compared the speed of light in the direction of the earth's motion with the speed at right angles to it. Presumably, if the aether existed and the earth were moving through it, the speed of light plus the speed of the earth's motion through it would add and the two would not agree.

However, the two did agree and Michaelson proposed the the measuring apparatus shrank in length due to the speed of the earth.

So by the time Einstein was working on the theory of relativity, the speed of light was well known and Michaelson's experiments showed that it was constant irrespective of any movement through the aether.

Einstein took these two results and others and ran the ball past the goal posts. He said forget the aether, we don't need it and c, the speed of light, is constant for all observers. He then showed all sorts of remarkable things followed. These effects, gravity bending spacetime, increased mass at high speed, time dilation have been experimentally verified to very precise degrees.:teacher:

[SkepticalScience]

Thanks for your answers, but this is still a bit odd to me.

I share many of the questions that Pragmatist brought up. Why would your mass go to INFINITE when you get closer to light? I can understand that your mass could increase as you accelerate but can't understand how your mass would become infinite.

Also, does light accelerate? When I turn on my flashlight, does light actually accelerate from 0 to 186,000mps or does it just INSTANTLY arrive at 186,000mps.

I can't imagine it would work instantly - but there are many supposed truths about light that boggle my imagination.

[IIRichard]

Originally posted by SkepticalScience
Thanks for your answers, but this is still a bit odd to me.

I share many of the questions that Pragmatist brought up. Why would your mass go to INFINITE when you get closer to light? I can understand that your mass could increase as you accelerate but can't understand how your mass would become infinite.

Also, does light accelerate? When I turn on my flashlight, does light actually accelerate from 0 to 186,000mps or does it just INSTANTLY arrive at 186,000mps.

I can't imagine it would work instantly - but there are many supposed truths about light that boggle my imagination.

The quick answer is that you can't get to the speed of light and therefore the mass approaches infinite but never quite gets there. The reason is e=mc^2. As more energy is put into the particle, spaceship, whatever, to push it closer and closer to the speed of light, that energy increases the mass.

As far as I know, a photon, a "particle" of light, is always at the speed of light from the instant of its creation except in certain laboratory environments.
:teacher:

[Dustin Kesselberg]

Originally posted by IIRichard
The quick answer is that you can't get to the speed of light and therefore the mass approaches infinite but never quite gets there. The reason is e=mc^2. As more energy is put into the particle, spaceship, whatever, to push it closer and closer to the speed of light, that energy increases the mass.

As far as I know, a photon, a "particle" of light, is always at the speed of light from the instant of its creation except in certain laboratory environments.
:teacher:


He is asking WHY it approaches infinite mass at the speed of light.

[CurtC]

Originally posted by 69dodge
Since spacetime is Galilean, nothing prevents one observer from moving at "c" relative to another. Then what? One observer sees the other keeping pace with a wave, while the other sees the wave passing himself at "c"?

I don't get it at all. [/B]Ah, yes you do! Your example is the perfect vehicle to understand why, in a universe where c is constant for all observers, it's impossible to ever attain c. Your example can't happen, because of the reason you describe - nothing with mass can ever go exactly c. Yours is a reductio ad absurdum explanation of why.

Dustin, Einstein already knew the speed of light to a high degree of accuracy, and that it seemed to be constant no matter what speed the obervers were going in. Further, Maxwell's equations, which seemed to do a really good job of describing electromagnetism, implied that c is a fixed constant no matter who is doing the measuring - those equations have c, and they didn't seem to specify which reference frame it was for.

It should have been obvious to everyone that the speed of light is constant for all observers. It's just that when you make that assumption, you get strange effects (such as time occuring at different paces for different observers), which everyone thought were ridiculous. Einstein had the genius to stick with it, and to grind through the math of what the world would be like if that assumption were true. His genius is that he followed where the science led him, and didn't automatically stick with his preconceptions. When he did grind through all that math, the equation e=mc^2 fell out into his lap. Something else that fell out was that apparent mass increases as an object approaches the speed of light, and as it gets closer, the mass increases without bound.

Understandably, this made a lot of physicists uncomfortable. But it sure resolved the issue of the speed of light and reference frames, and further, detailed predictions of the idea's time dilation effects were confirmed by measurements.

[rppa]

Originally posted by IIRichard
The quick answer is that you can't get to the speed of light and therefore the mass approaches infinite but never quite gets there. The reason is e=mc^2. As more energy is put into the particle, spaceship, whatever, to push it closer and closer to the speed of light, that energy increases the mass.

As far as I know, a photon, a "particle" of light, is always at the speed of light from the instant of its creation except in certain laboratory environments.
:teacher:

Not to throw too much confusion in here, but physicists no longer use the term "relativistic mass", nor do they talk about "mass increasing", nor do they use E = mc^2. The term "mass" is reserved for the invariant mass, or rest mass. So it is true that it takes infinite energy for an object with mass to achieve the speed of light, but not that the "mass" becomes infinite. For particles with nonzero mass, the modern version of Einstein's famous equation is E = gamma*mc^2.

Even Einstein himself was trying to get away from the whole "relativistic mass" usage, since he said it created more confusion than it resolved.

[IIRichard]

Originally posted by rppa
Not to throw too much confusion in here, but physicists no longer use the term "relativistic mass", nor do they talk about "mass increasing", nor do they use E = mc^2. The term "mass" is reserved for the invariant mass, or rest mass. So it is true that it takes infinite energy for an object with mass to achieve the speed of light, but not that the "mass" becomes infinite. For particles with nonzero mass, the modern version of Einstein's famous equation is E = gamma*mc^2.

Even Einstein himself was trying to get away from the whole "relativistic mass" usage, since he said it created more confusion than it resolved.

Thanks:)

[drkitten]

Originally posted by SkepticalScience

I share many of the questions that Pragmatist brought up. Why would your mass go to INFINITE when you get closer to light? I can understand that your mass could increase as you accelerate but can't understand how your mass would become infinite.


Your mass-energy becomes closer to infinite as your speed becomes closer to that of light. Mathematically, this can be expressed as as a formula in which the term (c - v) appears in the denominator of a fraction. When c > v, then the term is finite, but gets smaller and smaller as v gets closer to c. Dividing by a smaller and smaller number results in a larger and larger overall energy -- if v actually were equal to c, you would be dividing by zero, which gives an "infinite" overall energy.

For a physical intuition about how it happens, you can think about the amount of work it takes to accelerate a heavy object compared to a light object. Trucks don't accelerate as fast as cars, which don't accelerate as fast as motorcycles. But since adding energy makes something heavier, the faster it is going, the harder it is to accelerate further -- and, like Zeno's hare, you never actually catch up to the speed of light.

Alternatively, you can think of it in terms of length contraction and time dialation. As you get closer and closer to the speed of light, your meters get shorter and your seconds get longer. So an acceleration of 10 m/s is "really" (to an outside observer) 10 millimeters per hour, or 10 nanometers per month. Again, you will never actually catch up, because the faster you go, the smaller your "real" acceleration is.

[bigred]

Originally posted by Darat
When?



His genius.



When?



He didn't.
Don't you love it when someone gives pointless non-answers to questions in a (failed) attempt to look clever and witty OMG LMAO

:rolleyes:

[Darat]

Originally posted by bigred
Don't you love it when someone gives pointless non-answers to questions in a (failed) attempt to look clever and witty OMG LMAO

:rolleyes:

You forget your question mark. ;)

[SkepticalScience]

Oh - interesting post new drkitten.

So if (c-v) is in the denominator of the fraction - isn't that just a result of how the equation was set up?


A zero as a denominator is Undefined, not infinite. Meaning, that

1/0 does not equal 5/0. It just invalid. . .not infinite.

So maybe it's an urban legend that your mass approaches infinity. Because I still haven't heard, what happens at the molecular level that causes your mass to increase.

I mean, do your protons get larger or something? And if so - why?

[drkitten]

Originally posted by SkepticalScience
Oh - interesting post new drkitten.

So if (c-v) is in the denominator of the fraction - isn't that just a result of how the equation was set up?

A zero as a denominator is Undefined, not infinite. Meaning, that

1/0 does not equal 5/0. It just invalid. . .not infinite.


You're not treating the math properly. The expression 1/0 is undefined, but the limit of the quanitity 1/x, as x approaches 0, is well-defined as being infinite. Or if your analysis teacher didn't permit you to regard infinity as an actual limit value, then you can express that the value 1/x increases without limit as x approaches zero.

So as the difference (c-v) approaches zero, your mass-energy increases without limit.


So maybe it's an urban legend that your mass approaches infinity. Because I still haven't heard, what happens at the molecular level that causes your mass to increase.

I mean, do your protons get larger or something? And if so - why?

They get more energetic, and since energy and (relativistic) mass are equivalent (sorry, rppa), they are therefore more massive. And it's not just your protons, but everything about you. Again, a more formal statement is that you are gaining energy (by accelerating).

[rppa]

Originally posted by new drkitten
They get more energetic, and since energy and (relativistic) mass are equivalent (sorry, rppa), they are therefore more massive. And it's not just your protons, but everything about you. Again, a more formal statement is that you are gaining energy (by accelerating).

Two good summaries from the sci.physics FAQ:


If you go too fast, do you become a Black Hole? (http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/black_fast.html)

In part the misunderstanding arises because of the use of the concept of relativistic mass in the equation E = mc2. Relativistic mass, which increases with the velocity and kinetic energy of an object, cannot be blindly substituted into formulae such as the one that gives the radius for a black hole in terms of its mass. One way to avoid this is to not speak about relativistic mass and think only in terms of invariant rest mass.

and
Does mass change with velocity? (http://math.ucr.edu/home/baez/physics/Relativity/SR/mass.html)

Despite the general usage of invariant mass in the scientific literature, the use of the word mass to mean relativistic mass is still found in many popular science books. For example, Stephen Hawking in A Brief History of Time writes "Because of the equivalence of energy and mass, the energy which an object has due to its motion will add to its mass." and Richard Feynman in The Character of Physical Law wrote "The energy associated with motion appears as an extra mass, so things get heavier when they move." Evidently, Hawking and Feynman and many others use this terminology because it is intuitive and useful when you want to explain things without using too much mathematics. The standard convention followed by some physicists seems to be: use invariant mass when doing research and writing papers for other physicists but use relativistic mass when writing for non-physicists. It is a curious dichotomy of terminology which inevitably leads to confusion.

In a 1948 letter to Lincoln Barnett, Einstein wrote
"It is not good to introduce the concept of the mass M = m/(1-v^2/c^2)^1/2 of a body for which no clear definition can be given. It is better to introduce no other mass than `the rest mass' m. Instead of introducing M, it is better to mention the expression for the momentum and energy of a body in motion."

[phildonnia]

Originally posted by Terry
Well, it's high enough level to be somewhat portable, but close enough to the machine to do system programming.

Oh, not the programming language? never mind...


--Terry.

That was my first thought. Anyway the correct answer is:

1) It's a powerful antioxidant, and was endorsed by Linus Pauling for prevention of the common cold
2) The natural tones of the key contain no sharps or flats, so it's easiest to learn on a keyboard instrument
3) It's for "cookie", that's good enough for me.