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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby doogly » Fri Dec 13, 2013 2:24 am UTC

Though it bears noting that we define the speed of light and measure the meter.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby Yakk » Fri Dec 13, 2013 3:12 am UTC

Or the second?
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby doogly » Fri Dec 13, 2013 3:15 am UTC

The meter is defined in terms of the speed of light and the second, and the second is defined as the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby dudiobugtron » Tue Dec 17, 2013 4:19 am UTC

gmalivuk wrote:I suspect that the time the process of reflection takes is on the same order as the time it takes light to go the thickness of the reflecting surface, isn't it?


I don't personally know, but it sounds like most people here do! (So, I guess I do too, now.)
I wasn't sure how long it took for the whole process to happen, other than that it happened too fast for my eye to discern any difference.
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Question about Speed of light and The Distance Traveled

Postby fremen » Wed Jan 15, 2014 3:16 am UTC

I have read about time distortions caused by traveling close to or exceeding the speed of light. The hypothetical result would be that the stationary observer would either be left in the past or the future in reference to the object in motion.

Is there a minimum distance or time the object would have to traverse in relation to the stationary observer to be affected by the temporal distortion?

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Re: Question about Speed of light and The Distance Traveled

Postby Eebster the Great » Wed Jan 15, 2014 5:33 am UTC

fremen wrote:I have read about time distortions caused by traveling close to or exceeding the speed of light. The hypothetical result would be that the stationary observer would either be left in the past or the future in reference to the object in motion.

Is there a minimum distance or time the object would have to traverse in relation to the stationary observer to be affected by the temporal distortion?

Time dilation is caused by a relative difference in velocity, not by distance. Everything moving relative to you is also experiencing time more slowly (in your reference frame), and the faster they are moving the greater the dilation.

If you are sitting on Earth watching a spaceship fly away from it toward Alpha Centauri at 0.99 c, the crew of the spaceship will appear to be moving in slow motion. Although you will see the ship traveling for well over 4 years, the crew will only experience a little more than 7 months. From the reference frame of the ship, it is the Earth and Alpha Centauri which are moving so slow, while they are experiencing time normally. But Alpha Centauri will seem very close, only about 0.6 light years away (rather than 4.3 lightyears from the reference frame of either star (they are roughly comoving)). So it will still take you only 7 months to get there.

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby gmalivuk » Wed Jan 15, 2014 6:10 pm UTC

And the important thing to remember is that there is no minimum. Someone moving a couple miles per hour relative to you is, in your frame, experiencing time *slightly* more slowly. We can ignore it because we don't care that a million years for them would be a million years plus one second to you, but there's still a difference.

(Another reason we can ignore it in everyday life is that all the little differences average out to an even smaller difference than if thw motion was kept constant forever. Even at relativistic speeds, if I leave and return, and then my twin leave and return on the same trip at the same speed, we'll be back to the same age as each other again.)
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby fremen » Wed Jan 15, 2014 11:52 pm UTC

What if we could mechanically couple an object that would reverberate at a frequency at or exceeding the speed of light, moving back and forth within a short distance (say 50 nanometers) in relation to a stationary object.

Would there be a measurable effect?

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby eternauta3k » Thu Jan 16, 2014 12:38 am UTC

frequency at or exceeding the speed of light
Would there be a measurable effect?
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby phlip » Thu Jan 16, 2014 1:00 am UTC

fremen wrote:at or exceeding the speed of light

Relativity doesn't really say anything about such things... we can't really make scientific statements about them, because they are never observed.

It doesn't make sense to talk about time dilation for things that travel at the speed of light, because things that travel at the speed of light can never travel at any speed other than the speed of light, so the question becomes "time is dilated compared to what?"... things that actually have a rest mass can't be accelerated up to light speed, and massless particles like photons can only travel at light speed, and don't have any at-rest characteristics at all, simply because they can't be at rest.

Whereas for particles exceeding the speed of light, we only have baseless speculation... none have ever been observed, and there's no empirical reason to suspect they exist at all. There exist any number of extrapolations of relativity that allow for them, but they're just conjecture without any real scientific weight. Fun, but ultimately meaningless. It is however a consequence of things that do have a lot of evidence, that a massive object travelling slower than light can't accelerate to become faster than light... if tachyons do exist, they're a different form of matter that always travels faster than light, just like our regular massive matter always travels slower than light.

What is a more relevant question is what your reverberating object would do at speeds close to (but still less than) the speed of light. In which case: yes, it would be a measurable effect. Exactly how fast it would need to be before you'd have a measurable effect depends on how precise your measurements are, but at any speed it would have a non-zero effect, and as it approaches the speed of light, the effect will increase without bound.

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby Eebster the Great » Thu Jan 16, 2014 1:42 am UTC

I'd be a bit careful with the general statement that massless particles can travel "only" at c. As everyone knows, photons move more slowly through a medium than through a vacuum. Of course, the precursor still travels at c, but the front itself travels at a different speed that depends on the refractive index.

In terms of relativistic effects though, what you say is of course true.

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby some_dude » Thu Jan 16, 2014 2:06 am UTC

I actually asked that question some time ago in this same thread. The answer I got back then (by starslayer) was that photons always move at c.

Photons always exist at c; the explanation you heard [photons getting absorbed and then re-emitted with a slight delay] is actually correct. Why doesn't it result in severe distortion? Phase. Hecht's Optics devotes basically an entire chapter to explaining this, but here's a shorter version:

In a semi-classical picture, you can think of the atoms in a material as driven electric dipole oscillators. To start with, imagine you have a tenuous gas. This of course results in Rayleigh scattering of an optical light beam passing through it. Each molecule, when hit by a photon, immediately absorbs and reradiates it into an effectively random direction (yeah, electrodynamics comes in to make it non-isotropic, but bear with me here). So now we have a bunch of atoms radiating constantly into 4pi. However, consider the phase of the scattered wave at two points, A and B, in front of the beam and somewhere off to the side, respectively. Scattered light reaching A hasn't had it's path changed much by the scattering molecules, so the light is still roughly in phase. What about light at B, though? Now, the path lengths from B to each scatterer are radically different; the light reaches B with random phase. This fact that the wavelets emitted by the molecules are basically independent of each other in any direction except forward will be important in a second. Anyway, you can see that light is going to stream out of the beam; at low optical density, you get a strong forward beam and scattered light everywhere.

But what happens when we make the medium denser? What happens when the molecules are separated by less than the wavelength of light, as they are in a dense gas like sea-level air, or a liquid or solid? Since the original beam is effectively immediately completely absorbed when it hits the surface of such a medium, why are substances transparent at all?* Well, the picture at point A is much the same: the wavelets from the molecules are in-phase in the forward direction, and this constructive interference allows the beam to continue forward effectively unchanged in a transparent medium. At point B, however, you won't see much at all! Why? Now that the atoms/molecules are much closer together, you can no longer ignore the phase difference between two wavelets: the phase difference is now fractions of a wavelength, not many times the wavelength as it was in the tenuous medium. Because the wavelets are out of phase in all directions but forward, destructive interference predominates, and virtually no light is scattered out of the beam, nor is much energy lost. This interference and small spacing between scatterers is what allows the beam to travel through a dense medium without much distortion. In fact, the denser and more uniform the medium is, the more effective transmission becomes. This is why well-made glass or carefully made ice can be transparent on kilometer scales, while liquid water scatters everything away within a couple hundred meters.

*The answer to this has to do with resonances; the energy of optical photons is generally far from the transition energies for things like water, glass, etc. Since driving forces with frequencies far from resonance are not very efficient drivers, you don't get as much absorption and scattering. If you go into the infrared, for example, water molecules suddenly have a lot of transitions/resonances there, and water becomes opaque. Metals are a different kettle of fish.

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby PM 2Ring » Thu Jan 16, 2014 2:55 am UTC

FWIW, gold looks golden rather than silvery-white because of relativistic effects.

From http://en.wikipedia.org/wiki/Relativist ... nd_caesium
Color of gold and caesium

The reflectivity of Au, Ag, Al is shown on the figure to the right. The human eye sees electromagnetic radiation with a wavelength near 600 nm as yellow. As is clear from its reflectance spectrum, gold appears yellow because it absorbs blue light more than it absorbs other visible wavelengths of light; the reflected light (which is what we see) is therefore lacking in blue compared to the incident light. Since yellow is complementary to blue, this makes a piece of gold appear yellow (under white light) to human eyes.

The electronic transition responsible for this absorption is a transition from the 5d to the 6s level. An analogous transition occurs in Ag but the relativistic effects are lower in Ag so while the 4d experiences some expansion and the 5s some contraction, the 4d-5s distance in Ag is still much greater than the 5d-6s distance in Au because the relativistic effects in Ag are smaller than those in Au. Thus, non-relativistic gold would be white. The relativistic effects are raising the 5d orbital and lowering the 6s orbital.[11]

A similar effect occurs in caesium metal, the heaviest of the alkali metals which can be collected in quantities sufficient to allow viewing. Whereas the other alkaline metals are silver-white, cesium metal has a distinctly golden hue.

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby yurell » Thu Jan 30, 2014 9:07 pm UTC

Just asking this here because I don't think it deserves its own thread, but can an electron/positron annihilation result in three or more photons being emitted? If so, have we ever observed it? And if not, why can't it (afaik it still conserves all the required properties)?
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby Eebster the Great » Thu Jan 30, 2014 9:14 pm UTC

I don't see how three photons could conserve spin.

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby Yakk » Thu Jan 30, 2014 9:52 pm UTC

Wikipedia says "yes, but with lower probabilities".
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby WibblyWobbly » Thu Jan 30, 2014 10:41 pm UTC

Apparently when positronium annihilates, singlet configurations generate even numbers of photons (but mostly 2), and triplet configurations generate odd numbers (but mostly 3). But you can't get a single photon.

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby Dopefish » Thu Jan 30, 2014 10:58 pm UTC

So, regarding the implications of causality breaking FTL travel...

It's been awhile, but I gather relativity basically says that given the means to go FTL, one could arrange that in some frames messages could be received before they were sent, so that's bad and this is a pretty strong reason to believe FTL isn't possible.

Would it be correct to say the outcome of FTL travel is that for any given frame, someones present could be influenced by future events?

Is there a distinction to be made between future events being able to effect the present, and 'time travel' being possible as it's commonly depicted in sci-fi (as in people walking backwards and eggs unbreaking and everything runs in reverse for awhile)?

I think there is, but I'm not sure if one is just a more extreme example of the same principle if one looked close enough. The future events influencing the present seems maybe feasible as long as one isn't under any illusions of free will and we'd just get equations of motion that have (t+a) dependence or something along those lines, but actually making t go backwards seems like an entirely different thing.

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby Eebster the Great » Fri Jan 31, 2014 2:43 am UTC

Dopefish wrote:people walking backwards and eggs unbreaking and everything runs in reverse for awhile

That's a simple violation of the second law of thermodynamics.

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby Yakk » Fri Jan 31, 2014 3:45 am UTC

Which happens all the time, just on small scales.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby PM 2Ring » Fri Jan 31, 2014 5:01 am UTC

Eebster the Great wrote:I don't see how three photons could conserve spin.

Leptons have spin ½, photons have spin 1, so if the spins of the electron & positron are parallel (ortho-positronium) annihilation must create an odd number of photons, if they are anti-parallel (para-positronium) then annihilation must create an even number of photons.

Production of a single photon via ortho-positronium decay is impossible, since that would violate conservation of linear momentum, unless some other particle (or body) is involved in the interaction. This is a Good Thing, since it means that free photons don't tend to spontaneously decay into positronium. :)

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby yurell » Fri Jan 31, 2014 5:13 am UTC

PM 2Ring wrote:Leptons have spin ½, photons have spin 1, so if the spins of the electron & positron are parallel (ortho-positronium) annihilation must create an odd number of photons, if they are anti-parallel (para-positronium) then annihilation must create an even number of photons.


Does this just mean that the ortho- state is incredibly unlikely then?
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby PM 2Ring » Fri Jan 31, 2014 5:49 am UTC

yurell wrote:
PM 2Ring wrote:Leptons have spin ½, photons have spin 1, so if the spins of the electron & positron are parallel (ortho-positronium) annihilation must create an odd number of photons, if they are anti-parallel (para-positronium) then annihilation must create an even number of photons.


Does this just mean that the ortho- state is incredibly unlikely then?


AFAIK, both states are roughly equally likely, assuming the leptons aren't constrained by an external magnetic field as they meet. But I Am Not A Quantum Physicist.

When a random positron meets a random electron they effectively measure each other's spin, so there are only two possible outcomes, parallel & anti-parallel, with each outcome having a probability of 0.5.

However, ortho-positronium does have a much longer half-life than para-positronium (142 nanoseconds vs 125 picoseconds). I'm not quite sure why; I think it has something to do with Pauli exclusion, since two electrons (or two positrons) of parallel spin can't occupy the same position-momentum state, but an anti-parallel pair can.

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby WibblyWobbly » Fri Jan 31, 2014 8:13 am UTC

PM 2Ring wrote:
yurell wrote:
PM 2Ring wrote:Leptons have spin ½, photons have spin 1, so if the spins of the electron & positron are parallel (ortho-positronium) annihilation must create an odd number of photons, if they are anti-parallel (para-positronium) then annihilation must create an even number of photons.


Does this just mean that the ortho- state is incredibly unlikely then?


AFAIK, both states are roughly equally likely, assuming the leptons aren't constrained by an external magnetic field as they meet. But I Am Not A Quantum Physicist.

When a random positron meets a random electron they effectively measure each other's spin, so there are only two possible outcomes, parallel & anti-parallel, with each outcome having a probability of 0.5.

However, ortho-positronium does have a much longer half-life than para-positronium (142 nanoseconds vs 125 picoseconds). I'm not quite sure why; I think it has something to do with Pauli exclusion, since two electrons (or two positrons) of parallel spin can't occupy the same position-momentum state, but an anti-parallel pair can.


I thought I remembered reading somewhere that two-photon emission was many times more probable than three-photon (or at least seen far more frequently, hence the common idea that electron-positron annihilation produces two photons), but I'm likely less of a quantum physics expert than you are.

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby Carlington » Fri Jan 31, 2014 10:42 am UTC

If I'm following correctly, then it makes perfect sense that two-photon emission would be more likely. Since the probability of creating ortho-positronium and the probability of creating para-positronium are both 0.5, we're likely to, on average, end up with equal amounts of each being created. Since para-positronium has a much shorter half-life, we'll see para-positronium decay events far more frequently, and thus we'll see far more two-photon emissions in an arbitrary time period than we will three-photon emissions.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby yurell » Fri Jan 31, 2014 11:05 am UTC

Carlington wrote:If I'm following correctly, then it makes perfect sense that two-photon emission would be more likely. Since the probability of creating ortho-positronium and the probability of creating para-positronium are both 0.5, we're likely to, on average, end up with equal amounts of each being created. Since para-positronium has a much shorter half-life, we'll see para-positronium decay events far more frequently, and thus we'll see far more two-photon emissions in an arbitrary time period than we will three-photon emissions.


I don't understand that. If I send off a million positrons and wait a second, surely I should get half a million 2-photon and half a million 3-photon emissions, so why would we see more 2-photon?
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby Carlington » Fri Jan 31, 2014 2:10 pm UTC

I'm definitely much less of a quantum physicist than almost anyone else here, but my understaninding is that we're sending off a million positroniums (positronia?), as in a bound electron/positron pair, half of which are para-positronium and half of which are ortho-positronium. Then we wait a second, and since para-positronium has a much shorter half-life, it will be much higher and so we'll see many more decay events matching its emission signature in that second.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby Eebster the Great » Fri Jan 31, 2014 11:26 pm UTC

Well with a half-life of 142 nanoseconds, after a full second over 7 million half-lives would have passed, which would mean none of the original electron-positron pairs would remain, and thus you would not see any decays at all one second later.

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby yurell » Fri Jan 31, 2014 11:55 pm UTC

Sorry, when I said 'wait a second' I meant 'observe for a second'. Surely every piece of positronium would have decayed, and I would see equal amounts of two- and three-photon decay? Or am I missing some subtlety?
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby Eebster the Great » Sat Feb 01, 2014 12:35 am UTC

If both decays have 0.5 probability then by definition they will occur equally often.

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby yurell » Sat Feb 01, 2014 1:49 am UTC

Then I am confused. If there's an equal chance of the ortho- and para- states (here), why does 3-photon emission happen with lower probability (here)? Obviously I'm missing something, so if you have to explain it to me like I'm an idiot please do.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby PM 2Ring » Sat Feb 01, 2014 2:38 am UTC

Yakk wrote:Wikipedia says "yes, but with lower probabilities".

The Wiki article states that ortho-positronium has a longer mean lifetime than para-positronium, so in that sense 2 photon decay has a higher probability of occuring than 3 photon decay, but of course spontaneous conversion of one type of positronium to the other cannot occur, so I don't see why that's particularly relevant.

Hey, I could be wrong when I claimed that formation of ortho- and para- positronium are equiprobable: it's quite possible that the Pauli effects I mentioned earlier favour para-positronium production. Pity that the Wikipedia article doesn't discuss this question.

I've been trying to find a reference that does discuss the ratio of ortho- to para- positronium production for free electrons & positrons, but without success, although there are various articles that discuss positronium production via other mechanisms, eg relativistic collision of heavy nuclei. According to cds.cern.ch/record/372554/files/9811494.pdf‎ (page 20), Au-Au collision yields a para:ortho ratio of 1.7 : 1.4, Pb-Pb collision yields 155:48, but Ca-Ca is 1650:35. Unfortunately, most of that article is way over my head.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby Eebster the Great » Sat Feb 01, 2014 3:44 am UTC

Yurell you're right, those two statements are incompatible. Either the two are equiprobable or they are not, and I suspect it is the latter.

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby Carlington » Sat Feb 01, 2014 10:02 am UTC

Looking back through, my post was inconsistent. Sorry for confusing things further, yurell and everybody. My statements are only true in the case that we're observing, and all of the positronium has not yet decayed.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby lgw » Fri Feb 14, 2014 9:31 pm UTC

fremen wrote:What if we could mechanically couple an object that would reverberate at a frequency at or exceeding the speed of light, moving back and forth within a short distance (say 50 nanometers) in relation to a stationary object.

Would there be a measurable effect?


Old question, but no one had linked Cherenkov Radiation so I figured I would. Vibrating faster than the speed of light in some medium happens every day in nuclear reactors, and is pretty.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby Eebster the Great » Fri Feb 14, 2014 9:56 pm UTC

When you say a "frequency" faster than the speed of light, do you mean a "speed" faster than the speed of light?

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby Carlington » Sat Feb 15, 2014 1:09 am UTC

I think what's meant is an object that oscillates with a frequency and amplitude such that its overall velocity is greater than c.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby Eebster the Great » Sat Feb 15, 2014 1:31 am UTC

Again, by velocity you must mean speed. The average velocity of an oscillating object is the zero vector.

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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby doogly » Sat Feb 15, 2014 1:44 am UTC

No, nobody ever wants to use "speed." It just sounds so unsophisticated. It's worth like no points in Scrabble.
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Re: RELATIVITY QUESTIONS! (and other common queries)

Postby Eebster the Great » Sat Feb 15, 2014 2:20 am UTC

doogly wrote:No, nobody ever wants to use "speed." It just sounds so unsophisticated. It's worth like no points in Scrabble.

"Velocity" is a pretty difficult word to achieve in Scrabble, now that I think about it.


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