Limiting Light Speed?

Southwind17 · 24th August 2009, 10:50 AM

According to Stephen Hawking in "A Brief History of Time":

Quote:

The fundamental postulate of the theory of relativity, as it was called, was that the laws of science should be the same for all freely moving observers, no matter what their speed. This was true for Newton's laws of motion, but now the idea was extended to include Maxwell's theory and the speed of light: all observers should measure the same speed of light, no matter how fast they are moving. This simple idea has some remarkable consequences. Perhaps the best known are the equivalence of mass and energy, summed up in Einstein's famous equation E=mc² ... and the law that nothing may travel faster than the speed of light. Because of the equivalence of energy and mass, the energy which an object has due to its motion will add to its mass. In other words, it will make it harder to increase its speed. This effect is only really significant at speeds close to the speed of light. For example, at 10 percent of the speed of light an object's mass is only 0.5 percent more than normal, while at 90 percent of the speed of light it would be more than twice its normal mass. As an object approaches the speed of light, its mass rises ever more quickly, so it takes more and more energy to speed it up further. It can in fact never reach the speed of light, because by then its mass would have become infinite, and by the equivalence of mass and energy, it would have taken an infinite amount of energy to get it there. For this reason, any normal object is forever confined by relativity to move at speeds slower than the speed of light. Only light, or other waves that have no intrinsic mass, can move at the speed of light.

I acknowledge there have been threads regarding light speed, including a very recent one, however, the passage above raises a few questions in my mind that Hawking seems to leave hanging, and that I don't think were specifically addressed in such threads:

Did, and if so how, Hawking arrive at the example figures highlighted above simply by applying the formula E=mc²? If not, then how?
Both the example figures quoted and the statement highlighted indicate an indirectly proportional (exponential?) relationship between energy and mass, but doesn't E=mc² show a directly proportional relationship?
How does E=mc² dictate that m, and hence E, must both be infinite for an object to accelerate to speed c?
When scientists talk about the "speed of light" being a limiting speed for any object, do they mean the speed of light intrinsically (i.e. approx. 300,000km/s), or do they mean the speed of light conceptually? In other words, if the speed of light happened to be, say, 500,000km/s instead of 300,000km/s, which would be the limiting speed? Assuming it's 500,000km/s (which I suspect it is), how does one explain a seemingly arbitrary figure determining the speed at which an object can travel?
In a hypothetical (or possibly actual) dark corner of the universe where light doesn't exist (or, failing that, a parallel but "dark" universe), would it not be possible, without prior knowledge of light, to conclude the limiting speed of an object given the apparent absence of a scale of reference?
Acknowledging at least the idea of "relativity", if a space module were to be launched from the nose of a rocket travelling at 1km/s slower than the speed of light and the module travelled ahead of and away from the rocket at 2km/s compared to the rocket, what speeds would a single relatively static observer observe both the rocket and the space module travelling at?

Any enlightenment (pun intended) would be appreciated, ideally by reference only to the quoted passage, if practicable, but in any event commensurate with Hawking's claimed endeavour when he penned the book:

Quote:

But modern science has become so technical that only a very small number of specialists are able to master the mathematics used to describe them. Yet the basic ideas about the origin and fate of the universe can be stated without mathematics in a form that people without a scientific education can understand. This is what I have attempted to do in the book. The reader must judge whether I have succeeded.

Hawking did, however, go on to effectively confess that he couldn't write the book without citing E=mc², but that's the only equation/mathematics that appear within the book, and then only for context. Perhaps the absence of further mathematics accounts for my questions being seemingly unanswered, which might indicate that Hawking failed in his endeavour. I'm minded to grant him the benefit of any possible doubt, though, at least for the time being!

Pink Booties · 24th August 2009, 10:54 AM

This ought to be one of those threads that is greatly educational. I can only answer some of it, and will just wait until the big guns come by.

Southwind17 · 24th August 2009, 10:56 AM

Originally Posted by Pink Booties

This ought to be one of those threads that is greatly educational. I can only answer some of it, and will just wait until the big guns come by.

You must read faster than the speed of light! Is that a different equation?!

Pink Booties · 24th August 2009, 10:58 AM

I scanned it for what I do know... but there are better responders who'd correct my shaky understanding anyhow.

Anyways, a prediction of excellence ITT.

drkitten · 24th August 2009, 11:04 AM

Originally Posted by Southwind17

Did, and if so how, Hawking arrive at the example figures highlighted above simply by applying the formula E=mc²? If not, then how?

He did not. The formula he used is M = m/sqrt(1 - v²/c²)

Quote:

Both the example figures quoted and the statement highlighted indicate an indirectly proportional (exponential?) relationship between energy and mass, but doesn't E=mc² show a directly proportional relationship?

It does. But a body moving at 90% of the speed of light has more than nine times the energy (and hence mass) of a body moving at 10% of the speed of light. What the mc² formula does not show is how to compare the energies (and hence masses) of two objects moving at different speeds.

Quote:

How does E=mc² dictate that m, and hence E, must both be infinite for an object to accelerate to speed c?

It doesn't. But the other formula does.

Quote:

When scientists talk about the "speed of light" being a limiting speed for any object, do they mean the speed of light intrinsically (i.e. approx. 300,000km/s), or do they mean the speed of light conceptually? In other words, if the speed of light happened to be, say, 500,000km/s instead of 300,000km/s, which would be the limiting speed? Assuming it's 500,000km/s (which I suspect it is), how does one explain a seemingly arbitrary figure determining the speed at which an object can travel?

Not a meaningful question. "If my grandmother had balls, would she be my grandfather?"

Quote:

In a hypothetical (or possibly actual) dark corner of the universe where light doesn't exist (or, failing that, a parallel but "dark" universe), would it not be possible, without prior knowledge of light, to conclude the limiting speed of an object given the apparent absence of a scale of reference?

Yes. First, we can make our own light (or other forms of light-speed things). Second, we can accelerate particles and observe that twice as much energy doesn't produce twice as much speed.

Quote:

Acknowledging at least the idea of "relativity", if a space module were to be launched from the nose of a rocket travelling at 1km/s slower than the speed of light and the module travelled ahead of and away from the rocket at 2km/s compared to the rocket, what speeds would a single relatively static observer observe both the rocket and the space module travelling at?

The formula for addition of velocities is:

s = (v1 + v2) / [1+(v1/c)(v2/c)]

sol invictus · 24th August 2009, 11:12 AM

Originally Posted by Southwind17

Did, and if so how, Hawking arrive at the example figures highlighted above simply by applying the formula E=mc²? If not, then how?

The quantity Hawking is referring to is what's called "relativistic mass".
These days most physicists prefer to not use that term at all, as it creates precisely the questions you're asking. Anyway, to clarify: Hawking arrived at those results using the formula m_rel=gamma m₀, where gamma = (1-(v/c)²)^-1/2. m₀ is the rest mass of the object, v its speed.

The total energy of an object is E=m_relc² = gamma m₀ c².

Quote:

Both the example figures quoted and the statement highlighted indicate an indirectly proportional (exponential?) relationship between energy and mass, but doesn't E=mc² show a directly proportional relationship?

See above. It's not exponential, but it is a non-linear and increasing function of v.

Quote:

How does E=mc² dictate that m, and hence E, must both be infinite for an object to accelerate to speed c?

See the formula for gamma.

Quote:

When scientists talk about the "speed of light" being a limiting speed for any object, do they mean the speed of light intrinsically (i.e. approx. 300,000km/s), or do they mean the speed of light conceptually? In other words, if the speed of light happened to be, say, 500,000km/s instead of 300,000km/s, which would be the limiting speed? Assuming it's 500,000km/s (which I suspect it is), how does one explain a seemingly arbitrary figure determining the speed at which an object can travel?

There's a limiting speed, let's call it c. That's an experimental fact that's accounted for by relativity. There's also a speed of light. It turns out that the speed of light is c, but that's not the case for other waves (sound in air, for example). So it's perfectly possible to imagine a world where light moves slower than c (for example, it moves slower than c under water), but not one where it's faster.

Quote:

In a hypothetical (or possibly actual) dark corner of the universe where light doesn't exist (or, failing that, a parallel but "dark" universe), would it not be possible, without prior knowledge of light, to conclude the limiting speed of an object given the apparent absence of a scale of reference?

It would be possible to find the limiting speed c, sure.

Ziggurat · 24th August 2009, 11:29 AM

Originally Posted by Southwind17

[*]Both the example figures quoted and the statement highlighted indicate an indirectly proportional (exponential?) relationship between energy and mass, but doesn't E=mc² show a directly proportional relationship?

Depends what one means by mass. You can define a mass (known as "relativistic mass") for which E=mc² is always true. But this mass is velocity dependent.

One can also define a mass (known as the "invariant mass" or "rest mass") for which E=mc² is only true at zero velocity. This mass is not velocity dependent, but is always constant. The two masses are related via the equation drkitten gave (where M is relativistic mass and m is the invariant mass). There is a related equation which is always true for invariant mass: E²=m²c⁴ + p²c². This equation reduces to E=mc² for the case of p=0, but it also works for particles like photons which have zero invariant mass but nonzero momentum.

Relativistic mass was used in the early days of relativity because it made a number of relativistic equations look superficially like their old Newtonian counterparts. But it's actually awkward, and conceptually invariant mass is much more meaningful, so modern physicists have basically abandoned the use of relativistic mass in any actual work. Unfortunately its use has persisted when talking to non-physicist audiences, though.

Quote:

[*]When scientists talk about the "speed of light" being a limiting speed for any object, do they mean the speed of light intrinsically (i.e. approx. 300,000km/s), or do they mean the speed of light conceptually? In other words, if the speed of light happened to be, say, 500,000km/s instead of 300,000km/s, which would be the limiting speed?

Space and time have a particular relationship in relativity. This relationship is categorized by the ratio c, which happens to be about 3x10⁸ m/s. Any massless particle should travel at c (in a vacuum), light included, but there is nothing special about light in this regard, it's only the first and best known thing to travel at c. If c happened to be some other value, then light and any other massless particles would also travel at that other value.

Quote:

[*]In a hypothetical (or possibly actual) dark corner of the universe where light doesn't exist (or, failing that, a parallel but "dark" universe), would it not be possible, without prior knowledge of light, to conclude the limiting speed of an object given the apparent absence of a scale of reference?

The mechanics equations of relativity (momentum, kinetic energy, etc) include reference to c (actually, the ratio v/c). Careful measurement of the velocity dependence of these purely mechanical properties could allow one to deduce c without using light in any form.

Perpetual Student · 24th August 2009, 01:40 PM

Quote:

Relativistic mass was used in the early days of relativity because it made a number of relativistic equations look superficially like their old Newtonian counterparts. But it's actually awkward, and conceptually invariant mass is much more meaningful, so modern physicists have basically abandoned the use of relativistic mass in any actual work. Unfortunately its use has persisted when talking to non-physicist audiences, though.
Ziggurat

Why is that? Is it not still useful in analyzing the relationship between velocity and energy at velocities close to c in high energy accelerators, for example?

Ziggurat · 24th August 2009, 02:04 PM

Originally Posted by Perpetual Student

Why is that? Is it not still useful in analyzing the relationship between velocity and energy at velocities close to c in high energy accelerators, for example?

You can use it for that, but there's no need to, and it doesn't actually help. All it does is split the problem into two steps instead of a single step, you still end up doing the same amount of work. To make it more explicit, you can either do this:

M_rel = m₀/sqrt(1-v²/c²)
E = M_relc²

or this:

E = m₀c²/sqrt(1-v²/c²)

So working with relativistic mass provides no actual advantages. And it can cause all sorts of conceptual problems to novices (If I accelerate a particle to large enough speeds, will it become a black hole? No, it won't).

Perpetual Student · 24th August 2009, 02:23 PM

Originally Posted by Ziggurat

You can use it for that, but there's no need to, and it doesn't actually help. All it does is split the problem into two steps instead of a single step, you still end up doing the same amount of work. To make it more explicit, you can either do this:

M_rel = m₀/sqrt(1-v²/c²)
E = M_relc²

or this:

E = m₀c²/sqrt(1-v²/c²)

So working with relativistic mass provides no actual advantages. And it can cause all sorts of conceptual problems to novices (If I accelerate a particle to large enough speeds, will it become a black hole? No, it won't).

Makes sense, thanks. How about gravitational effects? Does not one have to take relativistic mass into account when calculating the gravitational effect on a particle traveling close to c by something gravitationally big, like a neutron star or black hole?

Ziggurat · 24th August 2009, 02:44 PM

Originally Posted by Perpetual Student

Makes sense, thanks. How about gravitational effects? Does not one have to take relativistic mass into account when calculating the gravitational effect on a particle traveling close to c by something gravitationally big, like a neutron star or black hole?

The gravitational field of a moving body is different than the gravitational field of a stationary body (see, for example, gravitomagnetism), so velocity absolutely makes a difference, but you're still using the invariant mass of the object, not its relativistic mass. In particular (as I already mentioned), you cannot turn an object into a black hole by making it go faster, regardless of how big its relativistic mass becomes. Whether or not an object is a black hole must be reference-frame independent.

Perpetual Student · 24th August 2009, 04:55 PM

Originally Posted by Ziggurat

The gravitational field of a moving body is different than the gravitational field of a stationary body (see, for example, gravitomagnetism), so velocity absolutely makes a difference, but you're still using the invariant mass of the object, not its relativistic mass. In particular (as I already mentioned), you cannot turn an object into a black hole by making it go faster, regardless of how big its relativistic mass becomes. Whether or not an object is a black hole must be reference-frame independent.

So, is it not true that one can use relativistic mass in Newton's law -- Gm₁m₂/r² -- to obtain the force of gravity? If not, would it give a close approximation?

Ziggurat · 24th August 2009, 05:09 PM

Originally Posted by Perpetual Student

So, is it not true that one can use relativistic mass in Newton's law -- Gm₁m₂/r² -- to obtain the force of gravity? If not, would it give a close approximation?

No, you cannot. In fact, for a moving mass the gravitational field isn't even spherically symmetric (and the Newtonian equation is a weak-field approximation to begin with). You can approximate it as symmetric if the velocity is low enough, in which case the relativistic mass is approximately the same as the rest mass as well, but it's always the rest mass, not the relativistic mass, which you use.

Perpetual Student · 24th August 2009, 05:19 PM

Originally Posted by Ziggurat

No, you cannot. In fact, for a moving mass the gravitational field isn't even spherically symmetric (and the Newtonian equation is a weak-field approximation to begin with). You can approximate it as symmetric if the velocity is low enough, in which case the relativistic mass is approximately the same as the rest mass as well, but it's always the rest mass, not the relativistic mass, which you use.

Thanks for your responses. So, since velocity is relative, both a particle and any larger object (e.g. star) would have non-spherical gravitational fields -- that's hard to visualize.
Relativistic mass seems to be a useless concept (or a wrong concept) -- if something as simple as substituting it in Newton's gravity equation gives meaningless results. OK, then.

Singularitarian · 24th August 2009, 05:25 PM

Originally Posted by Perpetual Student

Thanks for your responses. So, since velocity is relative, both a particle and any larger object (e.g. star) would have non-spherical gravitational fields -- that's hard to visualize.
Relativistic mass seems to be a useless concept (or a wrong concept) -- if something as simple as substituting it in Newton's gravity equation gives meaningless results. OK, then.

its not that relativistic mass is a wrong concept, but rather Newtonian equations only works as approximations. As approximations for low level velocities, Newtionian equations works quite well.

Ziggurat · 24th August 2009, 05:33 PM

Originally Posted by Perpetual Student

Thanks for your responses. So, since velocity is relative, both a particle and any larger object (e.g. star) would have non-spherical gravitational fields -- that's hard to visualize.

It's not that bad - the field is basically just squished along the direction of motion. This isn't unique to gravity either, the exact same thing happens to the electric field of a moving charge.
http://www.its.caltech.edu/~phys1/ja...ingCharge.html

Quote:

Relativistic mass seems to be a useless concept (or a wrong concept)

You can't really call it wrong since its definition is completely consistent, but yes, I think it's useless. It's redundant with energy, whereas rest mass is not.

makaya325 · 24th August 2009, 05:39 PM

Light speed may not be possible, but if one approaches the speed of light, will their body age quicker?

Ziggurat · 24th August 2009, 05:50 PM

Originally Posted by makaya325

Light speed may not be possible, but if one approaches the speed of light, will their body age quicker?

No - why would it?

makaya325 · 24th August 2009, 07:44 PM

Originally Posted by Ziggurat

No - why would it?

I have heard that if one approaches the speed of light, 5 minutes to them would be equal to something like 100 years, so would the person's body age normally or not?

CanadaGlass · 24th August 2009, 08:25 PM

Originally Posted by drkitten

we can accelerate particles and observe that twice as much energy doesn't produce twice as much speed.

I think it is worth noting which reference frame the energy is coming from. Admittedly, energy provided from the moving frame would have the same net effect, due to spacial compression, but I feel it is worth thinking about.

Ziggurat · 24th August 2009, 09:29 PM

Originally Posted by makaya325

I have heard that if one approaches the speed of light, 5 minutes to them would be equal to something like 100 years, so would the person's body age normally or not?

The person's body would age at the same rate their clock passed the time: it would be slow from our perspective, but normal from their perspective.

sol invictus · 24th August 2009, 09:36 PM

Originally Posted by CanadaGlass

I think it is worth noting which reference frame the energy is coming from. Admittedly, energy provided from the moving frame would have the same net effect, due to spacial compression, but I feel it is worth thinking about.

Energy can't "come from a reference frame". If there's an energy transfer it's there in all frames, but it's not "coming from" them.

hermite12 · 24th August 2009, 09:55 PM

An article in The New Scientist several months ago described the research of a physicist who claimed that the limiting speed of an object could be derived entirely through geometrical considerations, and had nothing to do with physics. What one finds is a limiting speed, but the theory doesn't say what the speed is. Physics does that.
Also, the speed of light is not constant; in a Bose-Einstein condensate, it is about the speed of a bicycle. In quantum experiments , it has been found possible to propel photons faster than the speed of light.

Ziggurat · 24th August 2009, 10:00 PM

Originally Posted by sol invictus

Energy can't "come from a reference frame". If there's an energy transfer it's there in all frames, but it's not "coming from" them.

He may be referring to the fact that the particular transfers of energy in an interaction are reference-frame dependent. For example, if a moving cue ball hits a stationary eight ball, the cue ball loses KE and the 8 ball gains KE. In the reference frame where the cue ball is initially at rest, however, it is the 8 ball which loses KE and the cue ball which gains KE.

sol invictus · 24th August 2009, 10:47 PM

Originally Posted by hermite12

An article in The New Scientist several months ago described the research of a physicist who claimed that the limiting speed of an object could be derived entirely through geometrical considerations, and had nothing to do with physics.

Geometry is physics.

Quote:

In quantum experiments , it has been found possible to propel photons faster than the speed of light.

Nope, not possible. Got a reference?

Originally Posted by Ziggurat

He may be referring to the fact that the particular transfers of energy in an interaction are reference-frame dependent. For example, if a moving cue ball hits a stationary eight ball, the cue ball loses KE and the 8 ball gains KE. In the reference frame where the cue ball is initially at rest, however, it is the 8 ball which loses KE and the cue ball which gains KE.

Well, I certainly agree that's correct (it caused horrible confusion in the DDWFTTW thread).

Southwind17 · 24th August 2009, 11:47 PM

Originally Posted by drkitten

Not a meaningful question. "If my grandmother had balls, would she be my grandfather?"

Mmm ... interesting, if somewhat bad-mannered, response, given that at least two people seem to have seen meaning in it and responded with civility. Hey ho.

Originally Posted by sol invictus

There's a limiting speed, let's call it c. That's an experimental fact that's accounted for by relativity. There's also a speed of light. It turns out that the speed of light is c, but that's not the case for other waves (sound in air, for example). So it's perfectly possible to imagine a world where light moves slower than c (for example, it moves slower than c under water), but not one where it's faster.

Originally Posted by Ziggurat

Space and time have a particular relationship in relativity. This relationship is categorized by the ratio c, which happens to be about 3x10⁸ m/s. Any massless particle should travel at c (in a vacuum), light included, but there is nothing special about light in this regard, it's only the first and best known thing to travel at c. If c happened to be some other value, then light and any other massless particles would also travel at that other value.

This is interesting, and enlightening - thanks to you both. So, if I understand correctly, there is nothing intrinsic about light that limits the speed of all other objects, almost the contrary, simply that light is subject to the same limitations that all other objects are. I've always assumed that there is something special about light that almost appears to act upon other objects thereby limiting their speed potential. However, I'm now left wondering what it is that dictates that limiting potential. I'm not hot on maths at the level normally encountered here in the Science Forum (hence my choosing Hawking's book to read), so can somebody simply explain why the limiting speed is not, say, 4x10⁸m/s instead of 3x10⁸m/s. Or, in other words, presumably, why the infinite energy point is reached at 3x10⁸m/s? I'd be happy to review a calculation, if that's relevant, provided it uses relative lay-person factors, or is otherwise easily explained. Thanks

Southwind17 · 24th August 2009, 11:55 PM

Incidentally, am I correct in thinking that radio waves, being massless (presumably), also travel at c? Is there anything intrinsically different about light and radio waves, or is it simply a different frequency?

How about electricity travelling through a conductor, in particular lightning (the speed at which a lightning fork travels from the point of origin to earth)? Sorry - just trying to contextualize. Thanks

Reality Check · 25th August 2009, 04:50 AM

Originally Posted by Southwind17

Incidentally, am I correct in thinking that radio waves, being massless (presumably), also travel at c? Is there anything intrinsically different about light and radio waves, or is it simply a different frequency?

How about electricity travelling through a conductor, in particular lightning (the speed at which a lightning fork travels from the point of origin to earth)? Sorry - just trying to contextualize. Thanks

You are correct. Radio waves are part of the electromagnetic spectrum. They are light of certain frequency range like infrared light, gamma rays, etc.
The speed of electricity through a conductor is the speed at which electrons can travel through the wire when under the influence of an electric field.

CanadaGlass · 25th August 2009, 05:00 AM

Originally Posted by sol invictus

Energy can't "come from a reference frame". If there's an energy transfer it's there in all frames, but it's not "coming from" them.

Makes sense. I realized the numbers would work out the same from either frame, but I neglected to realize the independence of the energy. Thanks.

CanadaGlass · 25th August 2009, 05:02 AM

Originally Posted by Ziggurat

He may be referring to the fact that the particular transfers of energy in an interaction are reference-frame dependent. For example, if a moving cue ball hits a stationary eight ball, the cue ball loses KE and the 8 ball gains KE. In the reference frame where the cue ball is initially at rest, however, it is the 8 ball which loses KE and the cue ball which gains KE.

Nope. sol got it.

ETA. You are correct in what you say, just that was not my point.

sol invictus · 25th August 2009, 09:11 AM

Originally Posted by Southwind17

, so can somebody simply explain why the limiting speed is not, say, 4x10⁸m/s instead of 3x10⁸m/s.

Annoying answer: the meter is defined by c. http://en.wikipedia.org/wiki/Metre

Marginally less annoying but much more profound answer: you can't ask questions like that (not if you want physics answers, at least). You're asking why a quantity with dimensions has the numerical value it does. The question is meaningless - it's like asking why we call north "north" instead of "gzzrft".

A meaningful question would be, "why is the ratio of the speed of light in vacuum to the limiting speed equal to 1?" (Note that ratios like that are dimensionless.)

hermite12 · 25th August 2009, 09:14 AM

.newscientist.com/article/mg19526173.500-photons-flout-the-light-speed-limit.html

hermite12 · 25th August 2009, 09:16 AM

newscientist.com/article/mg19526173.500-photons-flout-the-light-speed-limit.html

Ziggurat · 25th August 2009, 10:22 AM

Originally Posted by hermite12

.newscientist.com/article/mg19526173.500-photons-flout-the-light-speed-limit.html

I hate articles like this. They start out with this dramatic intro suggesting that a fundamental principle of physics is being toppled. But then towards the bottom we find,

"The photons don't violate relativity: it's just a question of interpretation.

Steinberg explains Nimtz and Stahlhofen's observations by way of analogy with a 20-car bullet train departing Chicago for New York. The stopwatch starts when the centre of the train leaves the station, but the train leaves cars behind at each stop. So when the train arrives in New York, now comprising only two cars, its centre has moved ahead, although the train itself hasn't exceeded its reported speed."

So no violation of relativity, and nothing is actually moving faster than c. It's neat, but not earth-shattering or even new (similar results can be found much earlier than 2007). But of course, that doesn't sell magazines, so they hype it out of proportion before admitting the more mundane truth.

sol invictus · 25th August 2009, 10:28 AM

Originally Posted by Ziggurat

So no violation of relativity, and nothing is actually moving faster than c.

From the article: "For the time being," he says, "this is the only violation [of special relativity] that I know of."

They attribute that quote to Nimtz. Either he's a crank that doesn't understand his own experiment or the New Scientist inserted [of special relativity] where it doesn't belong.

Knowing the NS, which is the Sun of science magazines, I strongly suspect the latter.

Southwind17 · 25th August 2009, 10:55 AM

Originally Posted by sol invictus

Annoying answer: the meter is defined by c. http://en.wikipedia.org/wiki/Metre

Annoying only in the sense that it doesn't really purport to answer the question as it has no relevance to time.

Originally Posted by sol invictus

Marginally less annoying but much more profound answer: you can't ask questions like that (not if you want physics answers, at least). You're asking why a quantity with dimensions has the numerical value it does. The question is meaningless - it's like asking why we call north "north" instead of "gzzrft".

Profound, certainly, but not sure I agree in principle. Let's assume, just for argument's sake, that similar to their being a limiting speed for an object there was also a limiting distance it could travel (at any speed) from its starting point, and let's assume that distance is 1km. What you seem to be suggesting here is that I'm seeking an answer to the question: why is 1km 1km? But that's not what I'm asking. I'm asking: why is the distance limited per se (even if we customarily called 1km "345gtds", say). BTW - I should not be surprised to learn, probably from an eminent linguistics scholar, that there's a perfectly rational reason why we call north "north", as opposed to anything else, especially "gzzrft"!

None of the mathematics I've seen so far seem to dictate, or maybe "support" is a better word, the limitation of speed to c. That could just be my limited mathematics capability, but if so I'm sure someone could show me the maths. Is it not possible to show a calculation where the answer comes out as 3x10⁸? If not, I'm beginning to think that E=mc² is not so worthy of the fame and respect that it receives, but no doubt there is something more profound about the equation that's eluding me, possibly, again, because of my limited mathematics capability.

Am I being unrealistic expecting sensible answers to such questions, by which I mean answers that a lay-person can relate to, and hence appreciate, as Hawking himself seemed to believe was possible? Or was Hawking being unrealistic, albeit with good intentions?

Originally Posted by sol invictus

A meaningful question would be, "why is the ratio of the speed of light in vacuum to the limiting speed equal to 1?" (Note that ratios like that are dimensionless.)

It would not be a meaningful question if you imagine for a moment that our universe was completely dark (i.e. no stars and no artificial light), and some creature (obviously that has emerged, evolved and survived in the complete absence of light!) claimed to have invented a spacecraft with a maximum speed of 4x10⁸. On what basis would you claim, and how would you show, that that's not possible?

Yoink · 25th August 2009, 11:03 AM

Originally Posted by sol invictus

From the article: "For the time being," he says, "this is the only violation [of special relativity] that I know of."

They attribute that quote to Nimtz. Either he's a crank that doesn't understand his own experiment or the New Scientist inserted [of special relativity] where it doesn't belong.

Knowing the NS, which is the Sun of science magazines, I strongly suspect the latter.

The title of Nimtz's paper is "Macroscopic Violation of Special Relativity," so I don't think this is New Scientist's error.

Derail: NS does do some pretty fluffy science reporting, but I also think they get a lot of unfair criticism. In this case they have a physicist who is specifically making a claim of having violated special relativity; how is that not going to be the headline and the lede? But they didn't simply credulously repeat they claim, they went and found another expert to lucidly debunk it. That all seems like responsible journalism.

Ziggurat · 25th August 2009, 11:09 AM

Originally Posted by Southwind17

None of the mathematics I've seen so far seem to dictate, or maybe "support" is a better word, the limitation of speed to c. That could just be my limited mathematics capability, but if so I'm sure someone could show me the maths.

OK. The energy of an object of nonzero rest mass m is given by
E = mc²/sqrt(1-v²/c²)
When v = 0, this reduces to the more well-known version, but that's not what you're interested in. What happens as v -> c? The term in the square root approaches zero, which means the denominator approaches zero, which means E approaches infinity. There's your limit: you can't put an infinite amount of energy into an object, so you can't get it to move at c. You can only approach c, and how close depends on how much energy you can pump into it.

Quote:

If not, I'm beginning to think that E=mc² is not so worthy of the fame and respect that it receives

The significance of that equation doesn't come from the limits it puts on speed - indeed, that equation alone indicates no speed limit at all. Rather, its significance comes from nuclear fusion. The variability of mass per nucleon for different elements was known experimentally, and given that equation, it became apparent that nuclear decays could release lots and lots of energy. It helped usher in the atomic age.

Quote:

It would not be a meaningful question if you imagine for a moment that our universe was completely dark (i.e. no stars and no artificial light), and some creature (obviously that has emerged, evolved and survived in the complete absence of light!) claimed to have invented a spacecraft with a maximum speed of 4x10⁸. On what basis would you claim, and how would you show, that that's not possible?

The equation I gave above. I already went over this in post #7.

sol invictus · 25th August 2009, 11:12 AM

Originally Posted by Southwind17

Let's assume, just for argument's sake, that similar to their being a limiting speed for an object there was also a limiting distance it could travel (at any speed) from its starting point, and let's assume that distance is 1km. What you seem to be suggesting here is that I'm seeking an answer to the question: why is 1km 1km? But that's not what I'm asking. I'm asking: why is the distance limited per se (even if we customarily called 1km "345gtds", say).

You would be justified in asking why there's a limiting distance. You would not be justified in asking why the limiting distance is 1km.

Quote:

BTW - I should not be surprised to learn, probably from an eminent linguistics scholar, that there's a perfectly rational reason why we call north "north", as opposed to anything else, especially "gzzrft"!

Sure - but you wouldn't get an explanation in terms of physics, because there isn't one.

Quote:

None of the mathematics I've seen so far seem to dictate, or maybe "support" is a better word, the limitation of speed to c.

Do you mean, "the existence of a limiting speed"? Otherwise we're back to square one.

Quote:

That could just be my limited mathematics capability, but if so I'm sure someone could show me the maths.

In special relativity, and in fact according to all the laws of physics as they are understood today, achieving speeds faster than c is mathematically impossible. E=gamma m c^2 is a good example, since gamma becomes infinite as the velocity approaches c.

Quote:

It would not be a meaningful question if you imagine for a moment that our universe was completely dark (i.e. no stars and no artificial light), and some creature (obviously that has emerged, evolved and survived in the complete absence of light!) claimed to have invented a spacecraft with a maximum speed of 4x10⁸. On what basis would you claim, and how would you show, that that's not possible?

The known laws of physics.

Originally Posted by Yoink

The title of Nimtz's paper is "Macroscopic Violation of Special Relativity," so I don't think this is New Scientist's error.

Wow. What an idiot. ETA: I see that paper hasn't been published, despite being on the arxiv for 2 years.

Option 1, then.

Ziggurat · 25th August 2009, 11:16 AM

Originally Posted by Southwind17

Incidentally, am I correct in thinking that radio waves, being massless (presumably), also travel at c?

Radio waves are just very long wavelength, low frequency light. So they are also made up of photons, and yes, they travel at c.

Quote:

Is there anything intrinsically different about light and radio waves, or is it simply a different frequency?

It's only a matter of frequency.

Quote:

How about electricity travelling through a conductor, in particular lightning (the speed at which a lightning fork travels from the point of origin to earth)? Sorry - just trying to contextualize. Thanks

That travels at less than c, sometimes considerably slower. Note, though, that there are often two velocities involved in a question like this: the signal velocity and the drift velocity. The latter is slower (often MUCH slower) than the former, but both are limited by c.

24th August 2009, 10:50 AM	#1
Southwind17 Illuminator Join Date: Sep 2007 Location: Location: Location Posts: 3,260	Limiting Light Speed? According to Stephen Hawking in "A Brief History of Time": Quote: The fundamental postulate of the theory of relativity, as it was called, was that the laws of science should be the same for all freely moving observers, no matter what their speed. This was true for Newton's laws of motion, but now the idea was extended to include Maxwell's theory and the speed of light: all observers should measure the same speed of light, no matter how fast they are moving. This simple idea has some remarkable consequences. Perhaps the best known are the equivalence of mass and energy, summed up in Einstein's famous equation E=mc² ... and the law that nothing may travel faster than the speed of light. Because of the equivalence of energy and mass, the energy which an object has due to its motion will add to its mass. In other words, it will make it harder to increase its speed. This effect is only really significant at speeds close to the speed of light. For example, at 10 percent of the speed of light an object's mass is only 0.5 percent more than normal, while at 90 percent of the speed of light it would be more than twice its normal mass. As an object approaches the speed of light, its mass rises ever more quickly, so it takes more and more energy to speed it up further. It can in fact never reach the speed of light, because by then its mass would have become infinite, and by the equivalence of mass and energy, it would have taken an infinite amount of energy to get it there. For this reason, any normal object is forever confined by relativity to move at speeds slower than the speed of light. Only light, or other waves that have no intrinsic mass, can move at the speed of light. I acknowledge there have been threads regarding light speed, including a very recent one, however, the passage above raises a few questions in my mind that Hawking seems to leave hanging, and that I don't think were specifically addressed in such threads: Did, and if so how, Hawking arrive at the example figures highlighted above simply by applying the formula E=mc²? If not, then how? Both the example figures quoted and the statement highlighted indicate an indirectly proportional (exponential?) relationship between energy and mass, but doesn't E=mc² show a directly proportional relationship? How does E=mc² dictate that m, and hence E, must both be infinite for an object to accelerate to speed c? When scientists talk about the "speed of light" being a limiting speed for any object, do they mean the speed of light intrinsically (i.e. approx. 300,000km/s), or do they mean the speed of light conceptually? In other words, if the speed of light happened to be, say, 500,000km/s instead of 300,000km/s, which would be the limiting speed? Assuming it's 500,000km/s (which I suspect it is), how does one explain a seemingly arbitrary figure determining the speed at which an object can travel? In a hypothetical (or possibly actual) dark corner of the universe where light doesn't exist (or, failing that, a parallel but "dark" universe), would it not be possible, without prior knowledge of light, to conclude the limiting speed of an object given the apparent absence of a scale of reference? Acknowledging at least the idea of "relativity", if a space module were to be launched from the nose of a rocket travelling at 1km/s slower than the speed of light and the module travelled ahead of and away from the rocket at 2km/s compared to the rocket, what speeds would a single relatively static observer observe both the rocket and the space module travelling at? Any enlightenment (pun intended) would be appreciated, ideally by reference only to the quoted passage, if practicable, but in any event commensurate with Hawking's claimed endeavour when he penned the book: Quote: But modern science has become so technical that only a very small number of specialists are able to master the mathematics used to describe them. Yet the basic ideas about the origin and fate of the universe can be stated without mathematics in a form that people without a scientific education can understand. This is what I have attempted to do in the book. The reader must judge whether I have succeeded. Hawking did, however, go on to effectively confess that he couldn't write the book without citing E=mc², but that's the only equation/mathematics that appear within the book, and then only for context. Perhaps the absence of further mathematics accounts for my questions being seemingly unanswered, which might indicate that Hawking failed in his endeavour. I'm minded to grant him the benefit of any possible doubt, though, at least for the time being!
	__________________ *How very dare you!* "England and America are two countries divided by a common language." - George Bernard Shaw (seconded by Southwind17) Last edited by Southwind17; 24th August 2009 at 10:53 AM.

24th August 2009, 10:56 AM	#3
Southwind17 Illuminator Join Date: Sep 2007 Location: Location: Location Posts: 3,260	Originally Posted by Pink Booties This ought to be one of those threads that is greatly educational. I can only answer some of it, and will just wait until the big guns come by. You must read faster than the speed of light! Is that a different equation?!
	__________________ *How very dare you!* "England and America are two countries divided by a common language." - George Bernard Shaw (seconded by Southwind17)

24th August 2009, 11:12 AM	#6
sol invictus Philosopher Join Date: Oct 2007 Location: Nova Roma Posts: 5,151	Originally Posted by Southwind17 Did, and if so how, Hawking arrive at the example figures highlighted above simply by applying the formula E=mc²? If not, then how? The quantity Hawking is referring to is what's called "relativistic mass". These days most physicists prefer to not use that term at all, as it creates precisely the questions you're asking. Anyway, to clarify: Hawking arrived at those results using the formula m_rel=gamma m₀, where gamma = (1-(v/c)²)^-1/2. m₀ is the rest mass of the object, v its speed. The total energy of an object is E=m_relc² = gamma m₀ c². Quote: Both the example figures quoted and the statement highlighted indicate an indirectly proportional (exponential?) relationship between energy and mass, but doesn't E=mc² show a directly proportional relationship? See above. It's not exponential, but it is a non-linear and increasing function of v. Quote: How does E=mc² dictate that m, and hence E, must both be infinite for an object to accelerate to speed c? See the formula for gamma. Quote: When scientists talk about the "speed of light" being a limiting speed for any object, do they mean the speed of light intrinsically (i.e. approx. 300,000km/s), or do they mean the speed of light conceptually? In other words, if the speed of light happened to be, say, 500,000km/s instead of 300,000km/s, which would be the limiting speed? Assuming it's 500,000km/s (which I suspect it is), how does one explain a seemingly arbitrary figure determining the speed at which an object can travel? There's a limiting speed, let's call it c. That's an experimental fact that's accounted for by relativity. There's also a speed of light. It turns out that the speed of light is c, but that's not the case for other waves (sound in air, for example). So it's perfectly possible to imagine a world where light moves slower than c (for example, it moves slower than c under water), but not one where it's faster. Quote: In a hypothetical (or possibly actual) dark corner of the universe where light doesn't exist (or, failing that, a parallel but "dark" universe), would it not be possible, without prior knowledge of light, to conclude the limiting speed of an object given the apparent absence of a scale of reference? It would be possible to find the limiting speed c, sure.
	Last edited by sol invictus; 24th August 2009 at 11:14 AM.

24th August 2009, 01:40 PM	#8
Perpetual Student Graduate Poster Join Date: Jul 2008 Location: USA Posts: 1,262	Quote: Relativistic mass was used in the early days of relativity because it made a number of relativistic equations look superficially like their old Newtonian counterparts. But it's actually awkward, and conceptually invariant mass is much more meaningful, so modern physicists have basically abandoned the use of relativistic mass in any actual work. Unfortunately its use has persisted when talking to non-physicist audiences, though. Ziggurat Why is that? Is it not still useful in analyzing the relationship between velocity and energy at velocities close to c in high energy accelerators, for example?
	__________________ $\xi$

24th August 2009, 02:04 PM	#9
Ziggurat Penultimate Amazing Join Date: Jun 2003 Posts: 13,873	Originally Posted by Perpetual Student Why is that? Is it not still useful in analyzing the relationship between velocity and energy at velocities close to c in high energy accelerators, for example? You can use it for that, but there's no need to, and it doesn't actually help. All it does is split the problem into two steps instead of a single step, you still end up doing the same amount of work. To make it more explicit, you can either do this: M_rel = m₀/sqrt(1-v²/c²) E = M_relc² or this: E = m₀c²/sqrt(1-v²/c²) So working with relativistic mass provides no actual advantages. And it can cause all sorts of conceptual problems to novices (If I accelerate a particle to large enough speeds, will it become a black hole? No, it won't).
	__________________ "There is certainly not one government in Europe but is now watching the war in this country, with the ardent prayer that the united States may be effectually split, crippled, and dismember'd by it... We are all too prone to wander from ourselves, to affect Europe, and watch her frowns and smiles. We need this hot lesson of general hatred, and henceforth must never forget it. Never again will we trust the moral sense nor abstract friendliness of a single government of the world." - Walt Whitman, 1864

24th August 2009, 10:54 AM	#2
Pink Booties Guest Join Date: Jan 2009 Location: in your guard, up on points, and stalling. Posts: 3,537	This ought to be one of those threads that is greatly educational. I can only answer some of it, and will just wait until the big guns come by.

24th August 2009, 10:58 AM	#4
Pink Booties Guest Join Date: Jan 2009 Location: in your guard, up on points, and stalling. Posts: 3,537	I scanned it for what I do know... but there are better responders who'd correct my shaky understanding anyhow. Anyways, a prediction of excellence ITT.

24th August 2009, 11:04 AM	#5
drkitten Penultimate Amazing Join Date: Mar 2004 Location: Wits' End Posts: 17,338	Originally Posted by Southwind17 Did, and if so how, Hawking arrive at the example figures highlighted above simply by applying the formula E=mc²? If not, then how? He did not. The formula he used is M = m/sqrt(1 - v²/c²) Quote: Both the example figures quoted and the statement highlighted indicate an indirectly proportional (exponential?) relationship between energy and mass, but doesn't E=mc² show a directly proportional relationship? It does. But a body moving at 90% of the speed of light has more than nine times the energy (and hence mass) of a body moving at 10% of the speed of light. What the mc² formula does not show is how to compare the energies (and hence masses) of two objects moving at different speeds. Quote: How does E=mc² dictate that m, and hence E, must both be infinite for an object to accelerate to speed c? It doesn't. But the other formula does. Quote: When scientists talk about the "speed of light" being a limiting speed for any object, do they mean the speed of light intrinsically (i.e. approx. 300,000km/s), or do they mean the speed of light conceptually? In other words, if the speed of light happened to be, say, 500,000km/s instead of 300,000km/s, which would be the limiting speed? Assuming it's 500,000km/s (which I suspect it is), how does one explain a seemingly arbitrary figure determining the speed at which an object can travel? Not a meaningful question. "If my grandmother had balls, would she be my grandfather?" Quote: In a hypothetical (or possibly actual) dark corner of the universe where light doesn't exist (or, failing that, a parallel but "dark" universe), would it not be possible, without prior knowledge of light, to conclude the limiting speed of an object given the apparent absence of a scale of reference? Yes. First, we can make our own light (or other forms of light-speed things). Second, we can accelerate particles and observe that twice as much energy doesn't produce twice as much speed. Quote: Acknowledging at least the idea of "relativity", if a space module were to be launched from the nose of a rocket travelling at 1km/s slower than the speed of light and the module travelled ahead of and away from the rocket at 2km/s compared to the rocket, what speeds would a single relatively static observer observe both the rocket and the space module travelling at? The formula for addition of velocities is: s = (v1 + v2) / [1+(v1/c)(v2/c)]

24th August 2009, 11:29 AM	#7
Ziggurat Penultimate Amazing Join Date: Jun 2003 Posts: 13,873	Originally Posted by Southwind17 []Both the example figures quoted and the statement highlighted indicate an indirectly proportional (exponential?) relationship between energy and mass, but doesn't E=mc² show a directly proportional relationship? Depends what one means by mass. You can define a mass (known as "relativistic mass") for which E=mc² is always true. But this mass is velocity dependent. One can also define a mass (known as the "invariant mass" or "rest mass") for which E=mc² is only true at zero velocity. This mass is not velocity dependent, but is always constant. The two masses are related via the equation drkitten gave (where M is relativistic mass and m is the invariant mass). There is a related equation which is always true for invariant mass: E²=m²c⁴ + p²c². This equation reduces to E=mc² for the case of p=0, but it also works for particles like photons which have zero invariant mass but nonzero momentum. Relativistic mass was used in the early days of relativity because it made a number of relativistic equations look superficially like their old Newtonian counterparts. But it's actually awkward, and conceptually invariant mass is much more meaningful, so modern physicists have basically abandoned the use of relativistic mass in any actual work. Unfortunately its use has persisted when talking to non-physicist audiences, though. Quote: []When scientists talk about the "speed of light" being a limiting speed for any object, do they mean the speed of light intrinsically (i.e. approx. 300,000km/s), or do they mean the speed of light conceptually? In other words, if the speed of light happened to be, say, 500,000km/s instead of 300,000km/s, which would be the limiting speed? Space and time have a particular relationship in relativity. This relationship is categorized by the ratio c, which happens to be about 3x10⁸ m/s. Any massless particle should travel at c (in a vacuum), light included, but there is nothing special about light in this regard, it's only the first and best known thing to travel at c. If c happened to be some other value, then light and any other massless particles would also travel at that other value. Quote: [*]In a hypothetical (or possibly actual) dark corner of the universe where light doesn't exist (or, failing that, a parallel but "dark" universe), would it not be possible, without prior knowledge of light, to conclude the limiting speed of an object given the apparent absence of a scale of reference? The mechanics equations of relativity (momentum, kinetic energy, etc) include reference to c (actually, the ratio v/c). Careful measurement of the velocity dependence of these purely mechanical properties could allow one to deduce c without using light in any form.
	__________________ "There is certainly not one government in Europe but is now watching the war in this country, with the ardent prayer that the united States may be effectually split, crippled, and dismember'd by it... We are all too prone to wander from ourselves, to affect Europe, and watch her frowns and smiles. We need this hot lesson of general hatred, and henceforth must never forget it. Never again will we trust the moral sense nor abstract friendliness of a single government of the world." - Walt Whitman, 1864

24th August 2009, 02:23 PM	#10
Perpetual Student Graduate Poster Join Date: Jul 2008 Location: USA Posts: 1,262	Originally Posted by Ziggurat You can use it for that, but there's no need to, and it doesn't actually help. All it does is split the problem into two steps instead of a single step, you still end up doing the same amount of work. To make it more explicit, you can either do this: M_rel = m₀/sqrt(1-v²/c²) E = M_relc² or this: E = m₀c²/sqrt(1-v²/c²) So working with relativistic mass provides no actual advantages. And it can cause all sorts of conceptual problems to novices (If I accelerate a particle to large enough speeds, will it become a black hole? No, it won't). Makes sense, thanks. How about gravitational effects? Does not one have to take relativistic mass into account when calculating the gravitational effect on a particle traveling close to c by something gravitationally big, like a neutron star or black hole?
	__________________ $\xi$ Last edited by Perpetual Student; 24th August 2009 at 02:24 PM.

24th August 2009, 02:44 PM	#11
Ziggurat Penultimate Amazing Join Date: Jun 2003 Posts: 13,873	Originally Posted by Perpetual Student Makes sense, thanks. How about gravitational effects? Does not one have to take relativistic mass into account when calculating the gravitational effect on a particle traveling close to c by something gravitationally big, like a neutron star or black hole? The gravitational field of a moving body is different than the gravitational field of a stationary body (see, for example, gravitomagnetism), so velocity absolutely makes a difference, but you're still using the invariant mass of the object, not its relativistic mass. In particular (as I already mentioned), you cannot turn an object into a black hole by making it go faster, regardless of how big its relativistic mass becomes. Whether or not an object is a black hole must be reference-frame independent.
	__________________ "There is certainly not one government in Europe but is now watching the war in this country, with the ardent prayer that the united States may be effectually split, crippled, and dismember'd by it... We are all too prone to wander from ourselves, to affect Europe, and watch her frowns and smiles. We need this hot lesson of general hatred, and henceforth must never forget it. Never again will we trust the moral sense nor abstract friendliness of a single government of the world." - Walt Whitman, 1864

24th August 2009, 04:55 PM	#12
Perpetual Student Graduate Poster Join Date: Jul 2008 Location: USA Posts: 1,262	Originally Posted by Ziggurat The gravitational field of a moving body is different than the gravitational field of a stationary body (see, for example, gravitomagnetism), so velocity absolutely makes a difference, but you're still using the invariant mass of the object, not its relativistic mass. In particular (as I already mentioned), you cannot turn an object into a black hole by making it go faster, regardless of how big its relativistic mass becomes. Whether or not an object is a black hole must be reference-frame independent. So, is it not true that one can use relativistic mass in Newton's law -- Gm₁m₂/r² -- to obtain the force of gravity? If not, would it give a close approximation?
	__________________ $\xi$

24th August 2009, 05:09 PM	#13
Ziggurat Penultimate Amazing Join Date: Jun 2003 Posts: 13,873	Originally Posted by Perpetual Student So, is it not true that one can use relativistic mass in Newton's law -- Gm₁m₂/r² -- to obtain the force of gravity? If not, would it give a close approximation? No, you cannot. In fact, for a moving mass the gravitational field isn't even spherically symmetric (and the Newtonian equation is a weak-field approximation to begin with). You can approximate it as symmetric if the velocity is low enough, in which case the relativistic mass is approximately the same as the rest mass as well, but it's always the rest mass, not the relativistic mass, which you use.
	__________________ "There is certainly not one government in Europe but is now watching the war in this country, with the ardent prayer that the united States may be effectually split, crippled, and dismember'd by it... We are all too prone to wander from ourselves, to affect Europe, and watch her frowns and smiles. We need this hot lesson of general hatred, and henceforth must never forget it. Never again will we trust the moral sense nor abstract friendliness of a single government of the world." - Walt Whitman, 1864

24th August 2009, 05:19 PM	#14
Perpetual Student Graduate Poster Join Date: Jul 2008 Location: USA Posts: 1,262	Originally Posted by Ziggurat No, you cannot. In fact, for a moving mass the gravitational field isn't even spherically symmetric (and the Newtonian equation is a weak-field approximation to begin with). You can approximate it as symmetric if the velocity is low enough, in which case the relativistic mass is approximately the same as the rest mass as well, but it's always the rest mass, not the relativistic mass, which you use. Thanks for your responses. So, since velocity is relative, both a particle and any larger object (e.g. star) would have non-spherical gravitational fields -- that's hard to visualize. Relativistic mass seems to be a useless concept (or a wrong concept) -- if something as simple as substituting it in Newton's gravity equation gives meaningless results. OK, then.
	__________________ $\xi$

24th August 2009, 05:25 PM	#15
Singularitarian Banned Join Date: Jul 2009 Posts: 1,008	Originally Posted by Perpetual Student Thanks for your responses. So, since velocity is relative, both a particle and any larger object (e.g. star) would have non-spherical gravitational fields -- that's hard to visualize. Relativistic mass seems to be a useless concept (or a wrong concept) -- if something as simple as substituting it in Newton's gravity equation gives meaningless results. OK, then. its not that relativistic mass is a wrong concept, but rather Newtonian equations only works as approximations. As approximations for low level velocities, Newtionian equations works quite well.
Singularitarian Banned Join Date: Jul 2009 Posts: 1,008

24th August 2009, 05:33 PM	#16
Ziggurat Penultimate Amazing Join Date: Jun 2003 Posts: 13,873	Originally Posted by Perpetual Student Thanks for your responses. So, since velocity is relative, both a particle and any larger object (e.g. star) would have non-spherical gravitational fields -- that's hard to visualize. It's not that bad - the field is basically just squished along the direction of motion. This isn't unique to gravity either, the exact same thing happens to the electric field of a moving charge. http://www.its.caltech.edu/~phys1/ja...ingCharge.html Quote: Relativistic mass seems to be a useless concept (or a wrong concept) You can't really call it wrong since its definition is completely consistent, but yes, I think it's useless. It's redundant with energy, whereas rest mass is not.
	__________________ "There is certainly not one government in Europe but is now watching the war in this country, with the ardent prayer that the united States may be effectually split, crippled, and dismember'd by it... We are all too prone to wander from ourselves, to affect Europe, and watch her frowns and smiles. We need this hot lesson of general hatred, and henceforth must never forget it. Never again will we trust the moral sense nor abstract friendliness of a single government of the world." - Walt Whitman, 1864

24th August 2009, 05:39 PM	#17
makaya325 Banned Join Date: Jan 2009 Location: It's ok, im a limo driver! Posts: 4,655	Light speed may not be possible, but if one approaches the speed of light, will their body age quicker?

24th August 2009, 05:50 PM	#18
Ziggurat Penultimate Amazing Join Date: Jun 2003 Posts: 13,873	Originally Posted by makaya325 Light speed may not be possible, but if one approaches the speed of light, will their body age quicker? No - why would it?
	__________________ "There is certainly not one government in Europe but is now watching the war in this country, with the ardent prayer that the united States may be effectually split, crippled, and dismember'd by it... We are all too prone to wander from ourselves, to affect Europe, and watch her frowns and smiles. We need this hot lesson of general hatred, and henceforth must never forget it. Never again will we trust the moral sense nor abstract friendliness of a single government of the world." - Walt Whitman, 1864

24th August 2009, 07:44 PM	#19
makaya325 Banned Join Date: Jan 2009 Location: It's ok, im a limo driver! Posts: 4,655	Originally Posted by Ziggurat No - why would it? I have heard that if one approaches the speed of light, 5 minutes to them would be equal to something like 100 years, so would the person's body age normally or not?

24th August 2009, 08:25 PM	#20
CanadaGlass Thinker Join Date: Aug 2009 Posts: 211	Originally Posted by drkitten we can accelerate particles and observe that twice as much energy doesn't produce twice as much speed. I think it is worth noting which reference frame the energy is coming from. Admittedly, energy provided from the moving frame would have the same net effect, due to spacial compression, but I feel it is worth thinking about.
CanadaGlass Thinker Join Date: Aug 2009 Posts: 211

24th August 2009, 09:29 PM	#21
Ziggurat Penultimate Amazing Join Date: Jun 2003 Posts: 13,873	Originally Posted by makaya325 I have heard that if one approaches the speed of light, 5 minutes to them would be equal to something like 100 years, so would the person's body age normally or not? The person's body would age at the same rate their clock passed the time: it would be slow from our perspective, but normal from their perspective.
	__________________ "There is certainly not one government in Europe but is now watching the war in this country, with the ardent prayer that the united States may be effectually split, crippled, and dismember'd by it... We are all too prone to wander from ourselves, to affect Europe, and watch her frowns and smiles. We need this hot lesson of general hatred, and henceforth must never forget it. Never again will we trust the moral sense nor abstract friendliness of a single government of the world." - Walt Whitman, 1864

24th August 2009, 09:36 PM	#22
sol invictus Philosopher Join Date: Oct 2007 Location: Nova Roma Posts: 5,151	Originally Posted by CanadaGlass I think it is worth noting which reference frame the energy is coming from. Admittedly, energy provided from the moving frame would have the same net effect, due to spacial compression, but I feel it is worth thinking about. Energy can't "come from a reference frame". If there's an energy transfer it's there in all frames, but it's not "coming from" them.

24th August 2009, 09:55 PM	#23
hermite12 New Blood Join Date: Jan 2008 Posts: 6	Is there a speed of light? An article in The New Scientist several months ago described the research of a physicist who claimed that the limiting speed of an object could be derived entirely through geometrical considerations, and had nothing to do with physics. What one finds is a limiting speed, but the theory doesn't say what the speed is. Physics does that. Also, the speed of light is not constant; in a Bose-Einstein condensate, it is about the speed of a bicycle. In quantum experiments , it has been found possible to propel photons faster than the speed of light.
hermite12 New Blood Join Date: Jan 2008 Posts: 6

24th August 2009, 10:00 PM	#24
Ziggurat Penultimate Amazing Join Date: Jun 2003 Posts: 13,873	Originally Posted by sol invictus Energy can't "come from a reference frame". If there's an energy transfer it's there in all frames, but it's not "coming from" them. He may be referring to the fact that the particular transfers of energy in an interaction are reference-frame dependent. For example, if a moving cue ball hits a stationary eight ball, the cue ball loses KE and the 8 ball gains KE. In the reference frame where the cue ball is initially at rest, however, it is the 8 ball which loses KE and the cue ball which gains KE.
	__________________ "There is certainly not one government in Europe but is now watching the war in this country, with the ardent prayer that the united States may be effectually split, crippled, and dismember'd by it... We are all too prone to wander from ourselves, to affect Europe, and watch her frowns and smiles. We need this hot lesson of general hatred, and henceforth must never forget it. Never again will we trust the moral sense nor abstract friendliness of a single government of the world." - Walt Whitman, 1864

24th August 2009, 10:47 PM	#25
sol invictus Philosopher Join Date: Oct 2007 Location: Nova Roma Posts: 5,151	Originally Posted by hermite12 An article in The New Scientist several months ago described the research of a physicist who claimed that the limiting speed of an object could be derived entirely through geometrical considerations, and had nothing to do with physics. Geometry is physics. Quote: In quantum experiments , it has been found possible to propel photons faster than the speed of light. Nope, not possible. Got a reference? Originally Posted by Ziggurat He may be referring to the fact that the particular transfers of energy in an interaction are reference-frame dependent. For example, if a moving cue ball hits a stationary eight ball, the cue ball loses KE and the 8 ball gains KE. In the reference frame where the cue ball is initially at rest, however, it is the 8 ball which loses KE and the cue ball which gains KE. Well, I certainly agree that's correct (it caused horrible confusion in the DDWFTTW thread).

24th August 2009, 11:47 PM	#26
Southwind17 Illuminator Join Date: Sep 2007 Location: Location: Location Posts: 3,260	Originally Posted by drkitten Not a meaningful question. "If my grandmother had balls, would she be my grandfather?" Mmm ... interesting, if somewhat bad-mannered, response, given that at least two people seem to have seen meaning in it and responded with civility. Hey ho. Originally Posted by sol invictus There's a limiting speed, let's call it c. That's an experimental fact that's accounted for by relativity. There's also a speed of light. It turns out that the speed of light is c, but that's not the case for other waves (sound in air, for example). So it's perfectly possible to imagine a world where light moves slower than c (for example, it moves slower than c under water), but not one where it's faster. Originally Posted by Ziggurat Space and time have a particular relationship in relativity. This relationship is categorized by the ratio c, which happens to be about 3x10⁸ m/s. Any massless particle should travel at c (in a vacuum), light included, but there is nothing special about light in this regard, it's only the first and best known thing to travel at c. If c happened to be some other value, then light and any other massless particles would also travel at that other value. This is interesting, and enlightening - thanks to you both. So, if I understand correctly, there is nothing intrinsic about light that limits the speed of all other objects, almost the contrary, simply that light is subject to the same limitations that all other objects are. I've always assumed that there is something special about light that almost appears to act upon other objects thereby limiting their speed potential. However, I'm now left wondering what it is that dictates that limiting potential. I'm not hot on maths at the level normally encountered here in the Science Forum (hence my choosing Hawking's book to read), so can somebody simply explain why the limiting speed is not, say, 4x10⁸m/s instead of 3x10⁸m/s. Or, in other words, presumably, why the infinite energy point is reached at 3x10⁸m/s? I'd be happy to review a calculation, if that's relevant, provided it uses relative lay-person factors, or is otherwise easily explained. Thanks
	__________________ *How very dare you!* "England and America are two countries divided by a common language." - George Bernard Shaw (seconded by Southwind17)

24th August 2009, 11:55 PM	#27
Southwind17 Illuminator Join Date: Sep 2007 Location: Location: Location Posts: 3,260	Incidentally, am I correct in thinking that radio waves, being massless (presumably), also travel at c? Is there anything intrinsically different about light and radio waves, or is it simply a different frequency? How about electricity travelling through a conductor, in particular lightning (the speed at which a lightning fork travels from the point of origin to earth)? Sorry - just trying to contextualize. Thanks
	__________________ *How very dare you!* "England and America are two countries divided by a common language." - George Bernard Shaw (seconded by Southwind17)

25th August 2009, 04:50 AM	#28
Reality Check Illuminator Join Date: Mar 2008 Location: New Zealand Posts: 4,363	Originally Posted by Southwind17 Incidentally, am I correct in thinking that radio waves, being massless (presumably), also travel at c? Is there anything intrinsically different about light and radio waves, or is it simply a different frequency? How about electricity travelling through a conductor, in particular lightning (the speed at which a lightning fork travels from the point of origin to earth)? Sorry - just trying to contextualize. Thanks You are correct. Radio waves are part of the electromagnetic spectrum. They are light of certain frequency range like infrared light, gamma rays, etc. The speed of electricity through a conductor is the speed at which electrons can travel through the wire when under the influence of an electric field.
	__________________ Real Science: NASA Finds Direct Proof of Dark Matter (another observation) (and Abell 520) "Our Undiscovered Universe" by Terence Witt: Review 1; Review 2

25th August 2009, 05:00 AM	#29
CanadaGlass Thinker Join Date: Aug 2009 Posts: 211	Originally Posted by sol invictus Energy can't "come from a reference frame". If there's an energy transfer it's there in all frames, but it's not "coming from" them. Makes sense. I realized the numbers would work out the same from either frame, but I neglected to realize the independence of the energy. Thanks.
CanadaGlass Thinker Join Date: Aug 2009 Posts: 211

25th August 2009, 05:02 AM	#30
CanadaGlass Thinker Join Date: Aug 2009 Posts: 211	Originally Posted by Ziggurat He may be referring to the fact that the particular transfers of energy in an interaction are reference-frame dependent. For example, if a moving cue ball hits a stationary eight ball, the cue ball loses KE and the 8 ball gains KE. In the reference frame where the cue ball is initially at rest, however, it is the 8 ball which loses KE and the cue ball which gains KE. Nope. sol got it. ETA. You are correct in what you say, just that was not my point.
CanadaGlass Thinker Join Date: Aug 2009 Posts: 211	Last edited by CanadaGlass; 25th August 2009 at 05:03 AM.

25th August 2009, 09:11 AM	#31
sol invictus Philosopher Join Date: Oct 2007 Location: Nova Roma Posts: 5,151	Originally Posted by Southwind17 , so can somebody simply explain why the limiting speed is not, say, 4x10⁸m/s instead of 3x10⁸m/s. Annoying answer: the meter is defined by c. http://en.wikipedia.org/wiki/Metre Marginally less annoying but much more profound answer: you can't ask questions like that (not if you want physics answers, at least). You're asking why a quantity with dimensions has the numerical value it does. The question is meaningless - it's like asking why we call north "north" instead of "gzzrft". A meaningful question would be, "why is the ratio of the speed of light in vacuum to the limiting speed equal to 1?" (Note that ratios like that are dimensionless.)

25th August 2009, 09:14 AM	#32
hermite12 New Blood Join Date: Jan 2008 Posts: 6	.newscientist.com/article/mg19526173.500-photons-flout-the-light-speed-limit.html
hermite12 New Blood Join Date: Jan 2008 Posts: 6

25th August 2009, 09:16 AM	#33
hermite12 New Blood Join Date: Jan 2008 Posts: 6	newscientist.com/article/mg19526173.500-photons-flout-the-light-speed-limit.html
hermite12 New Blood Join Date: Jan 2008 Posts: 6

25th August 2009, 10:22 AM	#34
Ziggurat Penultimate Amazing Join Date: Jun 2003 Posts: 13,873	Originally Posted by hermite12 .newscientist.com/article/mg19526173.500-photons-flout-the-light-speed-limit.html I hate articles like this. They start out with this dramatic intro suggesting that a fundamental principle of physics is being toppled. But then towards the bottom we find, "The photons don't violate relativity: it's just a question of interpretation. Steinberg explains Nimtz and Stahlhofen's observations by way of analogy with a 20-car bullet train departing Chicago for New York. The stopwatch starts when the centre of the train leaves the station, but the train leaves cars behind at each stop. So when the train arrives in New York, now comprising only two cars, its centre has moved ahead, although the train itself hasn't exceeded its reported speed." So no violation of relativity, and nothing is actually moving faster than c. It's neat, but not earth-shattering or even new (similar results can be found much earlier than 2007). But of course, that doesn't sell magazines, so they hype it out of proportion before admitting the more mundane truth.
	__________________ "There is certainly not one government in Europe but is now watching the war in this country, with the ardent prayer that the united States may be effectually split, crippled, and dismember'd by it... We are all too prone to wander from ourselves, to affect Europe, and watch her frowns and smiles. We need this hot lesson of general hatred, and henceforth must never forget it. Never again will we trust the moral sense nor abstract friendliness of a single government of the world." - Walt Whitman, 1864

25th August 2009, 10:28 AM	#35
sol invictus Philosopher Join Date: Oct 2007 Location: Nova Roma Posts: 5,151	Originally Posted by Ziggurat So no violation of relativity, and nothing is actually moving faster than c. From the article: "For the time being," he says, "this is the only violation [of special relativity] that I know of." They attribute that quote to Nimtz. Either he's a crank that doesn't understand his own experiment or the New Scientist inserted [of special relativity] where it doesn't belong. Knowing the NS, which is the Sun of science magazines, I strongly suspect the latter.