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Q & A: why constant speed of light

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Most recent answer: 09/17/2015
Q:
Why exactly is the speed of light constant in vacuum? I know that's what happens, but I want to know why. Relativity simply works under the assumption of light's constant speed, but that doesn't prove it. It's sort of like saying the product of two numbers is equal to the sum of the same two numbers just because 2+2=2x2. A proof requires more than a phenomenon.
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- Bill (age 16)
vancouver, BC, Canada
A:
This is an interesting philosophical question. In physics, we don't prove theories to be right, but we do prove theorems about the math used to hold together our theories. Which theories (whole structures, not just little fragmentary claims) are right is in the end determined by mere phenomena. Nobody gave us any book of true assertions, we have to cobble them together out of observation and mathematical logic.

The key logic behind Special Relativity was that Maxwell's equations for electromagnetism looked like exact, universal laws of physics, and their solution gives light waves with a universal speed. Now it was logically possible that those laws were only true in one special reference frame, but by 1905 no experiment (including the famous attempt by Michelson and Morley) provided any evidence that they failed to work in any inertial frame. Einstein showed that there was a logical, consistent framework (Special Relativity) in which Maxwell's equations worked in all inertial frames, and Newton's laws also almost worked for any objects moving slowly with respect to a frame. From this new framework, all sorts of other effects could be derived, and they were all confirmed. Among those many effects are the energy-dependent lifetimes of particles, the exact dynamics of fast-moving particles, the patterns of radiation from accelerating particles, the magnetism-like velocity-dependent term accompanying each fundamental force, etc.

Ultimately, the framework ran into trouble with gravity, and had to be replaced by General Relativity, which in turn probably will ultimately have to be replaced (maybe by something like String Theory) some day.

So in one sense you're right- we don't prove things the way mathematicians do, but instead have to rely a lot on what we actually see. In another sense you're wrong- we aren't generalizing from one isolated fact (like your numerical example), but fitting a huge collection of diverse observations precisely to an extended logical system.

Mike W.
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(published on 10/22/2007)

Follow-Up #1: How can photons be massless?

Q:
Thank you for your answer. However, youre still saying that light travels at constant speed because its an observation and works with all the theories. Is there a rational reasoning to this phenomenon? Also, I have another question regarding light. If light can be sucked into a black body, then it must have mass, no matter how little. Since light travels at light speed itself, wouldnt it have infinite mass? Thank you again for your time.
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- Bill (age 16)
Vancouver, BC, Canada
A:
Bill- Right, I'm still saying that light travels at a constant speed because that's an observation and that it fits in a coherent theory with all sorts of other detailed observations of diverse phenomena. I know this point is hard to take in emotionally, but that's all the justification we have for anything. Whatever other sort of 'rational reasoning' justification you were hoping for is not something we can provide for any assertion at all. Can you deduce the existence of a table from logical first principles?
What I suspect is that you think there is something irrational about saying that light's speed is constant, but I am not claiming the right to be irrational. The sense that relativity is irrational rests on some common-sense assumptions about the nature of space and time. It turns out those common-sense assumptions are just wrong, usable only as good approximations for a limited range of phenomena. Relativity is a set of precise rules for describing how space-time looks from different viewpoints, just as objective and definite and logically consistent as common-sense, but not the same set of rules as common-sense. One is right and the other is wrong, and observation is what tells us which is which.

Your question about light's mass raises an issue we've addressed here occasionally, where some confusion arises from two different ways that different physicists use the word 'mass'. If by 'mass' you mean 'the quantity that serves as a source for gravity' or 'the thing which you multiply velocity by to get momentum' or 'the thing which is equivalent to energy' then light has mass. If you mean 'the mass something has when viewed in a frame in which the thing is standing still' (sometimes called 'rest mass' or the 'invariant mass') then it has none. There is no frame in which the light is standing still, since (as we started with) its speed is constant. Its rest mass is zero.

If you tried to imagine something that had some rest mass and was traveling at the speed of light, it would have infinite "mass' of the first kind, or infinite energy. So things like that don't exist. There are zero-rest-mass things that always travel at c, and nonzero-rest-mass things that never travel at c.

Mike W.

Comparison of observation with the predictions of theories really is about as rational as it's possible to get.  One of the reasons is that the theories may turn out someday to be wrong, and we'd have to invent new ones, but the only reason we'd ever do that is to explain some observation that the current theories disagree with.  So far, it's been good with the photon having zero mass.  Some other experimental and theoretical ingredients (which you may find also elsewhere on this site) are given below.  A small mass to the photon will cause the electrostatic force law to deviate from its standard inverse-square version (Coulomb's law), and also change the shape of Earth's magnetic field.  The current upper bound on the photon mass is m(photon)<1E-52  kilograms (from the 2004 particle data booklet, see <a href="http://pdg.lbl.gov">http://pdg.lbl.gov</a>).

Given this observation, we can build theories which accommodate, and even require, the photon's masslessness.  Quantum electrodynamics (QED) has at its core a U(1) gauge symmetry -- every electron's wavefunction can be multiplied by a complex function of unit magnitude and which varies smoothly in space, but is otherwise arbitrary.  From this symmetry, all of electricity and magnetism can be derived, and it has been tested to exquisite precision, particularly in the quantum corrections to g-2 for the electron.  People have worked very hard to test it, and to see if the model breaks down anywhere, but it works very very well.  If someone measures a tiny photon mass someday, it'll all come crashing down and we'll have to invent another theory.  But we have evidence from high-energy particle collisions that this theory is just embedded in another beautiful model, the electroweak interaction, which describes the weak force, and the model is also spectacularly successful there too.  We keep testing things at the edge of our knowledge, and modifying our models as we go along.

Actually, the U(1) gauge symmetry argument is a little circular, in that it assumes special relativity's geometry of space and time, as well as quantum mechanics.  But it does identify the photon as the thing that travels at the speed of light (a similar symmetry applies to gluons, the massless carriers of the strong force).  No such symmetry was identified for the neutrinos, and while we thought they, too were massless (largely because we couldn't measure their masses for a long time because we didn't have a sensitive enough experiment), there was no compelling reason to believe they are massless.  It turns out that an experiment in the late 1990's showed at least some of the neutrinos have mass, and any model explaining why they were massless is now unviable.  But now we are stuck with the problem of explaining why their masses are so small compared with everything else.

  Tom

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(published on 10/22/2007)

Follow-Up #2: light near a black hole

Q:
Hi Mike: Sorry to "annoy" you again. You stated that when light travels at light speed, it has zero mass. If that must be true, can you explain the reason why light, when its traveling, gets sucked into a black hole. If light has zero mass when its traveling, then 0xinfinity=undefined, which doesnt comply with the observations of light and black body.
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- Bill (age 16)
Vancouver, BC, Canada
A:
Hi Bill- That's not quite what I wrote. I said that that a photon (a quantum of light) has zero 'rest mass', also called 'invariant mass'. Its energy (equivalent to a mass via E=mc2) is not zero. It is well defined, being hf where h is Planck's constant and f is the frequency of the light in your reference frame.  Light does serve as the source of a gravitational field. Semi-classically, then, you can think of it as having a gravitational mass and thus falling in a gravitational field.
That picture actually doesn't give the right answer, since a light beam curves by twice as much as it would if you just thought of it as a relativistic particle in a field in classical space time. The rest of the curvature of the beam comes from the non-Euclidean (curved) nature of space in General Relativity.

Mike W.
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(published on 10/22/2007)

Follow-Up #3: How do you measure the speed of light?

Q:
Hello, I would like to know if there is any record of how the speed of light has been measured/Estimated and the method used for this purpose.The answer to this question might help in understanding why the speed of light is constant further.
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- Ganesh
Bangalore,Karnataka, India
A:
There are a number of ways to measure the speed of light.   Historically the first measurement, with several percent accuracy, was performed in 1676 by the Danish astronomer Rmer who noticed discrepancies in the times of eclipses of the moons of the planet Jupiter as the earth revolved around the sun.  Earlier measurements were woefully wrong:  Galileo and others tried to compare the speed of light to that of sound, unsuccessfully.  The accuracy since Rmer's time has improved by orders of magnitude.  See:

The constancy of the speed of light is a different matter.  All experiments, both in the laboratory and in astronomical measurements, have verified that this is true.

LeeH
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(published on 01/02/2010)

Follow-Up #4: Does the speed of light change?

Q:
Hi, Thanks for the Reply!!. I Understand that the observations show the constancy of speed of light.Now I have another question.If we take the speed of light just after the big bang and the speed of light now, Is there a difference in the value of c?
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- Ganesh
Bangalore,Karnataka,India
A:
So far as we can tell, c has been fixed at least since a very short time after the Big Bang. When you get too close to the singularity (or whatever it actually was), we don't know what sort of laws held.

Mike W.
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(published on 01/02/2010)

Follow-Up #5: Why assume light speed is constant?

Q:
I used to believe that the speed of light was constant from all perspectives, therefore I assumed it was simple to prove. Since then, I have learned it is not constant from all perspectives, my first question is what makes light's speed different from anything else's speed. OK Im going back a few steps, but i was not satisfied with your answer of how it has been proven that lights speed is constant. First i would like to point out that the assumption that the speed of light is a constant is what allowed the present formulas and theories to be created; therefore obviously none of these formula can be used to prove the preceding presumption. That would be circular reasoning. Is there any experiment capable of demonstrating the consistency of the speed of light?
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- Craig (age 20)
Kelowna, B.C. Canada
A:
There may be two slightly different takes on what you're asking.

Earlier in this thread, we addressed the question of why we don't try to pick a special frame to call "at rest" and say that light only travels at c with respect to that frame. The reason is that we would end up saying that nature has conspired to change all sorts of other variables in exactly the way needed to prevent us from ever measuring anything that could tell us whether we're using that frame or not. (Poincare said just that.) If we try to define speed by using any physical objects at all to measure distance and time, the same physical objects give the same light speed for light going by us in any direction. Our neighbor who is moving past us tries the same measurements with identically constructed meter sticks and clocks, and gets the same speed. These sorts of measurements have been done repeatedly, starting with the famous Michelson-Morley experiment.

We could stubbornly insist that only one of those frames is the "correct" one, but that assertion would tell us nothing new and correct about anything we observe. Or we could postulate with Einstein that all laws of physics, including ones to be discovered, will look the same in each frame. That was a spectacularly successful prediction for the many laws that have been discovered since 1905.

Perhaps you're asking more about why we can't pick among some much broader set of coordinate choices, if we allow that light speeds in different directions don't have to be equal. I've heard that it is possible to construct such coordinates (here I'm discussing on small patches of spacetime, not the coordinates of General Relativity). Then obviously basic laws such as Maxwell's equations (from which the speed of light is derived) would need some messy form in which the spatial derivatives in different directions are multiplied by different factors and/or various extra terms are added in. Why would anybody choose such major complications, when the much simpler choice of having laws that are independent of spatial orientation works perfectly well?

To repeat a philosophical point- yes all of science involves some circular logic. There's no set of unquestionable axioms from which you can derive the whole thing. You try to find simple self-consistent rules and see which fit the phenomena.

Mike W.
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(published on 03/09/2011)

Follow-Up #6: Is speed of light zero?

Q:
Hi,I want to ask, Is it possible that the speed of light is zero and what we assume "speed of light is constant" is just expanding speed of our universe?.As we know that matter is deeply connected to space as a result we feel gravity,likewise light is also connected to space and when it is created it accelerates with the speed of expanding space because atoms are way too heavy when compared to light and light probably has the mass somewhat equivalent to that of space.(Just a hypothetical thought).
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- syd
Hyderabad,Andhrapradesh,India
A:
It's hard to see how you could make a consistent description with the speed of light being zero, since in any one region you have light rays going all different directions. How could each ray have speed of zero?

Mike W.
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Follow-Up #7: Does light have mass?

Q:
Still unsatisfied with the initial answers to the question: has light mass?. it is confusing the mixture of observation and concepts--term such as semi-classically. If light would has mass, agrees with light being sensitive to the space curvature or a black whole. However, this idea conflicts with the initial assumptions: Why then speed of light is constant? and why this is the maximal speed in the universe?
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- LEGO (age 50)
solon
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To the best of our knowledge, the standard picture we've presented is fully self-consistent. Light which is traveling in a particular direction has no invariant mass, i.e. E=pc, where E is energy and p is momentum. The E and p of the light enter into the General Relativistic gravity equations just like any other E and p. There's also a pressure term in GR, also directly obtainable from the dependence of E of light on a coordinate stretch.

The geodesic paths followed by light are just the limiting paths for any particles whose velocity approaches c. By "semi-classically" we just meant "pretending that space is Euclidean". It isn't, so that's why the real answer comes out different.

Could you follow up with an explanation of what inconsistency you believe you see?

Mike W.
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(published on 12/17/2011)

Follow-Up #8: different concepts of mass

Q:
Thanks so much for your answer on this fascinating topic. I was unsatisfied with the idea of formulating two separate concepts of mass that are not intuitive. '..the quantity that serves as a source for gravity' vs. 'the thing which you multiply velocity by to get momentum'. Are these supposed to be equivalent? ( a principle in general relativity?). We know that in the universe nothing is “still” but only in a reference frame; example: we are moving at the earth & galaxy speed of rotation & translation although we do not notice. Is such a movement part of an object momentum? Accordingly, I can understand that light moves faster because its momentum is much lower. However light is sensitive to gravity, for example light follows the geodesics in space. It is possible that neutrinos have even less mass, so they interact less with space curvature (gravity) and, therefore, they do not follow the earth warping space. Will this explain the fact that neutrinos may travels faster than light?
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- LEGO (age 50)
Solon, OH, USA
A:
Yes, the mass that appears in the gravity source term and the one that appears in the velocity-momentum ratio are the same thing. As you say, this equivalence is at the heart of General Relativity.

You also ask if GR effects on neutrino travel might give the apparent faster-than-light travel reported by the group from CERN. The answer is no. The total GR effects on the coordinates near Earth are only around one part per billion, much smaller than the discrepancy reported for neutrino speeds. Now it may be that there was some subtle problem with clock synchronization involving GR effects as a clock was slowly transported from the neutron source to the detector. However, no such effect on the fast-traveling neutrinos themselves could be nearly large enough to account for the reported anomaly.

Mike W.
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(published on 12/25/2011)

Follow-Up #9: deriving speed of light?

Q:
The first questioner Bill asked a question which might be interpreted as: can one derive the speed of light, and the fact that it is constant in all inertial frames, from theoretical first principles (rather than simply measuring it). You mentioned later that the velocity of light can be derived from Maxwell's equations, but this uses classical wave theory based on measured values and mathematical relations between charge density, current, and magnetic flux density, and also involves an implicit assumption of a "medium" or single inertial frame. In some sense, that Maxwell's equations work at all is kind of a coincidence, a classical approximation, because it doesn't take into account the underlying principles of relativity or quantum mechanics. Given these considerations, my question is: is there a way to derive the speed of light, and the fact that it is the same in all inertial frames, using only the notions of space, time, matter, and energy that are consistent with quantum theory?
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- Jeff (age 52)
Clovis, NM, USA
A:

There are really two questions there. One is whether the particular value for the speed of light can be derived from something deeper than Maxwell's equations, with their empirical constants. The current answer is no. In fact, it would hardly even mean anything to derive c, since it has units (e.g. m/s) and the number depends entirely on the units. What physicists ask is whether various dimensionless numbers (e.g. the fine structure constant) involving c can be derived from some deeper rule. The answer to that is still no, at least for now..

Your other question is whether there's a way to derive that c is constant in all inertial frames. At heart, that amounts to deriving the rules for transforming coordinates between the different frames. I believe the answer to that is also no currently. Perhaps a deeper theory will be developed from which the rules of relativity (such as the Lorentz transforms) will emerge.

Mike W.

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Follow-Up #10: thanks

Q:
Hi Mike! I don't have a follow up question, but I found this page searching for answers and just wanted to thank you for taking the time to answer the questions.
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- Aaron Von Gauss (age 38)
Boynton Beach, FL
A:
Aaron- we always publish notes like yours.

Mike W.
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(published on 11/01/2012)

Follow-Up #11: philosophy of relativity

Q:
Mike, I find that physics is easier to understand if you separate it into two distinct components. (1) There is an objective reality which we observe through phenomenon. (2) The mathematics of Physics, which are used to *model* and *simulate* the actual objective reality. I find that physicists assert (directly or indirectly) that the mathematics *is* the objective reality. This is tantamount to confusing a doll house with an actual home. The dollhouse is a *model* of the house, accurate in many details, but it can never be mistaken for an actual house. A dollhouse can be used to predict traffic patterns and determine furniture placement, but you will never eat in its kitchen nor sleep in the bedrooms. It is a place to play and tinker. One must always keep in mind is that the mathematics of physics is NOT objective reality. That is to say that Physics is the DOLLHOUSE that allows us to tinker with the math in order to describe and predict what is happening in the actual house of objective reality. So is the speed of light constant? Who knows what is happening in the objective reality? However, that assumption, allows for much simpler mathematics, the extension of relativity to electrodynamics, and the mathematics provides a better tool for predicting and modeling objective reality. Michael
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- Michael J. Schreck (age 51)
Danbury, CT, USA
A:
Thanks for the philosophical musings. I don't have definite views on those general questions, so I'll just pass yours on to other readers.

On the particular application to the question of relativity, you ask "...is the speed of light constant? Who knows what is happening in the objective reality?" Here I sort of disagree. Even asking the question of what something's speed is implicitly assumes some particular type of mathematical framework. So once you've gotten that far, I think it's ok to answer "yes".

Mike W.
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(published on 12/24/2012)

Follow-Up #12: fundamentals about light and relativity

Q:
Q1: Lots of fundamental constants in physics/mathematics end up being related to each other. Does the speed of light c enjoy any such reputation? Is there a beautiful power series expansion or a continued fraction expansion for c ? Q2: So when the light gets sucked into a black hole, it accelerates, but the acceleration doesn't change its speed? Q3: Do we ever talk of rate of change of acceleration (or may be other higher derivatives of distance) in special/general theory of relativity? If not, why not? Q4: Thought experiment 1: How does a photon see the rest of the universe? Does it observe different speeds, accelerations, etc? Q5: Thought experiment 2: Does a photon in a light beam sees a photon in another light beam tavelling at a constant speed c? What about the relative speed of two photons in the same beam of light? Q6: If light is never at rest, how do we define it? We still haven't been able to define motion (refer Zeno's arrow motion paradox), though certain people claim that calculus has settled it, but it hasn't.
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- Amarpal Singh (age 38)
Thousand Oaks, CA, USA
A:
Q1: Not really. "c" is usually given as a number in some arbitrary units, in which case the numerical value has no deep significance at all.  In fundamental units, we define c=1, which is special but not in a complicated way.

Q2: The speed as locally measured in a standard reference frame doesn't change. Whether you want to say the light "accelerated" or not is a matter of word choice, or more precisely on choice of coordinate system. In one standard coordinate system the light falling into a black hole slows down on the way in due to the gravitational redshift.

Q3. Even in classical physics the time derivative of the acceleration, called the "jerk", is sometimes referred to. In general relativity, I believe that it comes up as an important quantity in understanding the radiation from particles in reference frames in which there's a uniform gravitational acceleration. Choosing such a reference frame doesn't make a charged particle radiate, but a first look at the expressions for radiation makes it seem that any accelerated particle does radiate. So I guess that the jerk becomes useful in these descriptions.

Q4. Our coordinate transforms (Lorentz transforms in special relativity) don't include transforms to frames moving at c with respect to the initial frame. So I don't think there's a real answer to this.

Q5. The speed of light remains c in any of the special relativistic frames. Thus in the limit as you get close to the speed of light, according to the initial frame, it should remain c. It's not clear what it means to say two photons are in the same beam, but so long as you don't insist on knowing how things truly look from the photon's point of view, in that limit any other photon you look at is traveling at c.

Q6. I don't understand here what you're asking. What is it you want done? What do you mean by "define"?

Mike W.
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(published on 01/20/2013)

Follow-Up #13: pressure causing gravity in relativity

Q:
what is that pressure that you mentioned in follow up #7?
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- Bassem (age 18)
ramboland
A:
This pressure comes from the decrease in energy of photons when their wavelengths are stretched. It is just 1/3 of the photon energy density for an isotropic photon gas. That's because the energy is proportional to the magnitude of the momenta which go as the inverse of the wavelengths, which go as the cube root of the volume.

For a gas of slow-moving massive particles, the pressure is 2/3 the kinetic energy density. That's because that energy goes as the momenta squared.

Mike W.
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Follow-Up #14: questions about light reflection

Q:
You have addressed various questions about light, here's mine. How can the QM properties of light result in the "real world" phenomenon of image reflection observed in a mirror or window or flat surface of water? Here is a microscopic blob of energy - with wavelike properties measured in nanometers - traveling at incredible speed - that was initiated by my light bulb - and it "bounces off" of glass or some other reflective surface - at exactly the right angle - and forms an image of me shaving? If nothing else, the "bouncing off" of glass isn't the redirection of something moving at the speed of light, is it? Instead, reflection would seem to require an incoming photon being absorbed by a silicon or oxygen atom and then being reemitted again in a different direction, right? That process alone looks like it would result in a randomization of the outgoing photon direction, not precise reflection angles. So how can there be images formed? Also, is there a maximum number of photons that can exist in a given (small) volume of space? And why don't photons interact with each other? How can a photon travel for billions of years in a straight line and never get struck by another photon (or gas molecule, for that matter) and get deflected off course in a way that would spoil the ability of Hubble to form an image from it?
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- Ricky (age 57)
Huntsville AL 35803
A:
1.  "the "bouncing off" of glass isn't the redirection of something moving at the speed of light, is it?"
Yes, it is.

2. "reflection would seem to require an incoming photon being absorbed by a silicon or oxygen atom and then being reemitted again in a different direction, right?   That process alone looks like it would result in a randomization of the outgoing photon direction, not precise reflection angles.  So how can there be images formed?"
Absorption/re-emission processes (fluorescence) do indeed scramble the directions and thus ruin images. So that is not what happens in reflection. "Bouncing" is a much more accurate way to think of it.

3. "Also, is there a maximum number of photons that can exist in a given (small) volume of space? "
Yes, there are limits involving quantum gravity and black holes. Those limits are far above any photon density with which we ever expect to deal.

4. "why don't photons interact with each other? "
They do, but weakly.

5. "How can a photon travel for billions of years in a straight line and never get struck by another photon (or gas molecule, for that matter) and get deflected off course...? "
The photon-photon interactions are extremely weak for visible photons. The gas molecules and atoms are very sparse. Since the main ones around are hydrogen and helium, they  also interact quite weakly with visible light.

Mike W.
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(published on 03/04/2013)

Follow-Up #15: Is the speed of light zero?

Q:
My response considers your answer on : "Follow-Up #6: Is speed of light zero?" I was honestly appalled by the lack of sophistication of your answer. I don't personally know the theory this person was talking about, but it took me less than a minute to see where your own answer went wrong. I'll try to explain: Imagine a sphere within a sphere within a sphere within a sphere [=4 spheres]. Now imagine each sphere to be a possible beam of light [i.e. all quantumpossible variations of a beam of light]. Now look at the inner sphere; notice all 3 other spheres overlapping the inner sphere, i.e. all 4 lightbeams possibly crossing eachother. Honestly, 1 minute it took me to see. There might be other problems with this theory, but I certainly consider this one ripe for a bit more thinking about.
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- Taeke van der Sluis (age 42)
Netherlands
A:

I can't really follow your objection, or whether your picture is supposed to have spheres or spherical solids for the possible endpoints. Perhaps your point is that two light rays can start at the same spacetime point and end at the same spacetime point (within measurement accuracy), which would be consistent with assigning a velocity of zero to them both. Of course they can also end up at different places at the same time (in some frame). That's what usually happens, and it's inconsistent with their speed being zero.

Back in Missouri we didn't always consider sophistication to be a good thing.

Mike W.

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(published on 07/05/2013)

Follow-Up #16: light beams crossing

Q:
no, the point is simply that 2 lightbeams can still cross eachother, something you supposed to be impossible. The sphere you get when you assume a beginningpoint of a photon being the centre of the sphere, add all possible trajectories of this photon during a given time, these then form a sphere. Well, only if you assume space not to be warped of course. The point of course also is that a photon doesn't come into being until it interacts with another particle, before that it is just possible that it exists and doesn't exist at the same time, this has consequences for the idea of its 'trajectory'. but you're right the sphere you can imagine to be a solid but empty form, an adding up of endpoints of the photon after a given time. Another point of expanding space is that something can never end up at it's own startingpoint, since the point will have expanded to become something bigger. I must admit i have trouble totally visualizing this idea of space itself expand at lightspeed, but it is an interesting thought, and I also have trouble understanding relativity [i think it to be a mere patch on other theories, not having any underlying idea or vision, and i don't understand how you can still agree on anything [dates, distance between objects] after apllying it], and also i have trouble understanding quantumtheory, so in this respect i don't consider this trouble any reason for not further exploring the idea
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- Taeke van der Sluis (age 42)
Netherlands
A:

No, of course two light beams can cross. Our point was that if the speed of light were zero then if two light beams were at the same place at the same time they would always be at the same place at any time. Since that's false the speed of light can't be zero.

As for your lack of understanding of the beautiful simplicity of special relativity, what can we say? You should at least give it a try.

Mike W.

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(published on 07/08/2013)

Follow-Up #17: philosophy and physics

Q:
I got back to my curiosity concerning particle physics due to the relatively recent Higgs boson discovery and all that it encompasses, and because before i had ever heard of fields, i had a hard time agreeing to the fact that light travels as waves if there is no medium. i have always struggled with relativity given is counter intuitive claims apllied to real life. i can accept that its claims may become apparent in extreme cases of speed and mass and that its real life implications are so small they can be negligable in day to day life. that said, i find quite dissapointing that physics is inevitably based on assumptions because those assumptions seem to be coroborated by observations. that means that any conclusion extrapolatd from physics or math, how ever elegant it may be, may come crashing down when one day, some random discovery contradicts some fundamental rule like c=constant and turns the standard model to mush. that said, it seems quite pointless to debate diverging points of view because as odd as it may sound, whatever it is you defend may one day be proven right, or, contrarilly, as right as one may feel to be, he may tomorrow be very very wrong. i'd like to be wrong about my statement. thank you
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- cesar (age 30)
France
A:

Yes, but the debates are still of value. They can help us find out which views are already wrong today.

Mike W.

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(published on 07/17/2013)

Follow-Up #18: speed of reflecting photons

Q:
When a photon hits a mirror and is reflected, wouldn't a fast enough measuring device determine it's speed goes to zero and then back to light speed?
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- Don (age 60)
Arkansas
A:

Whether we choose to say it's the same photon after reflection or not is a little arbitrary, but I'll go along with saying it's the same. At any rate, any blip of light, single photon or whatever, has some spatial extent. So it doesn't reflect in an instant, but gradually as it arrives at the mirror. Catch the process halfway through and the expectation of the light momentum is indeed zero. However, that doesn't mean the momentum is zero. The momentum, like typical quantum variables, has a range of values. In this case the range includes a lump of values pointing the initial direction and a lump pointing the opposite way. Only the average is zero.

Mike W.

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(published on 07/18/2013)

Follow-Up #19: Is the speed of light constant in all directions?

Q:
Do the properties of Relativity prevent the use of measurement of light speed in various spatial directions to determine what speed and direction our galaxy is traveling within the universe; or determine our point of origin? Would we need to be moving at near the speed of light for measurements in one direction to cancel out and find the direction we are traveling? If we are farther from the center of a nearly infinite universe, are we more likely to detect the difference in light speed of two opposite direction beams because one beam travels the same path we are moving, and being so far from the center of the universe we are moving nearly the finite speed of light?
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- John Dees (age 55)
Ferriday, LA USA
A:

Many experiments have shown that the speed of light is a constant in all directions.   This is in agreement with the theory of Special Relativity.  

As to the movement of the earth and Milky Way with respect to the rest of the universe, please take a look at our answer to a previous question by typing  23242  into the search box. 

 

LeeH

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(published on 07/18/2013)

Follow-Up #20: reflecting photon velocity

Q:
Mike, thanks for your response. As a followup to my question, I understand a photon is defined as both an energy wave and a particle but shouldn't any and all parts of that wave reflecting actually go to a zero velocity at the point of reflection? If so, I would think that would change the overall speed of the photon therefore taking it below lightspeed. And if this is the case, doesn't that somewhat alter the theory that a photon can only travel at the "speed of light"? You also indicated that maybe it wasn't the same photon being reflected. Can you explain that mechanism?
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- Don (age 60)
Arkansas
A:

I don't think it's really meaningful to say what's happening to the wave "at the point of reflection". A point amounts to zero fraction of the wave. 100% of the wave is either moving at c one way or the opposite way.

On the question of the photon identity, I probably shouldn't have mentioned that distraction. There's no real question of fact to figure out, it's just a matter of naming convention. In some ways saying that the reflection gradually replaces one photon with a different one going the other way helps make it easier to not think of some particular object as changing direction. The basic facts don't depend on that choice of descriptions, however.

Mike W.

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(published on 07/19/2013)

Follow-Up #21: can you determine your absolute speed?

Q:
Just to follow up on the second last question, it doesn't seem the actual question was answered. Because C is absolute from any frame of reference due to time dilation, couldn't methods of measurement be used to determine the observer's speed? For example, when flying at 0.9c significant time dilation within atomic clocks will be measured, through precise clocks and mathematics couldn't we determine the exact amount of time dilation occurring and use it to compare our speed to c, giving us an absolute speed as well? Is there anything in relativity that prevents us from knowing our absolute speed using the absolute speed of light and time dilation? If not, couldn't we use this to decelerate to a true rest frame? (Sorry if this was submitted twice, website issues)
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- Kyle (age 21)
St. Albert, AB, Canada
A:

Your question gives us a good opportunity to go over some basics of special relativity. The observer cannot determine his own speed by checking his clock rate because every single one of his clocks, of all types, continue to agree with each other. He can look at other clocks passing by. They all look slow, just as his clocks look slow to them. None of this does anything at all to help find who is "at rest".  As far as special relativity is concerned, the phrase "at rest" is entirely meaningless. 

The velocity determinations discussed in some of our answers concerned velocity relative to the average of all our neighbors, represented by the cosmic microwave background, not relative to some abstract "space".

Mike W.

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(published on 08/18/2013)

Follow-Up #22: Does the speed of light change?

Q:
Hi, I've read almost all these questions and responses, so I hope you don't try to repeat any of those... I've learned that before the 1900's they actually measured at different times with different experiments the speed of light, and all those measurements show different speeds. It wasn't until the beginning of the 1900's they re-defined the "speed of light" and the measurements units were coupled to the speed of light. I ask you in that context; how could any measurements in any experiment afterwards, and dare I say, until this day, actually disprove that the speed of light is changing? It might still change, and we could not see it, because the units to measure the changes , change with it (because they are linked). I mean, I talked to a lot of scientists and all assume it's constant because that's what they are learned. Nobody every gave it a second thought either. On your page at least, I've found some references to experiments, that would actually proof it's constant, then again, if after that one (I don't care even if it's a dozen experiments) experiment, nobody dares to challenge it again ... it is the same with energy and matter, the assumption that the amounts don't change. Researching into it, I haven't found any good reference to any experiment that must prove it. In textbooks you can read it also actually is an assumption (based on that god created the atom and could not be split (atom, greeks, etc)). And so what if the universe actually grew? Larger and larger (like an organism), and energy levels and matter varies over time? It wouldn't need any dark matter or dark energy at all to explain expansion, let alone accelerating expansion... I'm happy to discuss that subject one day... I would to conclude be happy to have in your reply some links and references to actual experiments being carried out and their results that prove that light speed is a constant (not using units of measurements linked to the speed of light of course). You have referenced "experiments" in general, so I'm just curious. I do believe in science, that is also constantly "doubting" itself, without that doubt, how can any experiment lead to a definite answer? For your reference : "Increased accuracy of c and redefinition of the metre[edit source] See also: History of the metre In the second half of the 20th century much progress was made in increasing the accuracy of measurements of the speed of light, first by cavity resonance techniques and later by laser interferometer techniques. In 1972, using the latter method and the 1960 definition of the metre in terms of a particular spectral line of krypton-86, a group at NBS in Boulder, Colorado determined the speed of light in vacuum to be c = 299,792,456.21.1 m/s. This was 100 times less uncertain than the previously accepted value. The remaining uncertainty was mainly related to the definition of the metre.[Note 8][105] As similar experiments found comparable results for c, the 15th Confrence Gnrale des Poids et Mesures (CGPM) in 1975 recommended using the value 299,792,458 m/s for the speed of light.[135] In 1983 the 17th CGPM redefined the metre thus, "The metre is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second."[81] As a result of this definition, the value of the speed of light in vacuum is exactly 299,792,458 m/s[136][137] and has become a defined constant in the SI system of units.[11] Improved experimental techniques do not affect the value of the speed of light in SI units, but instead allow a more precise realization of the metre" So, I ask you again, if the speed were changing, and the unit we use to measure it, is the metre; based on above "assumption", we could not ever notice it, because "the metre is is the length of the path travelled by light in vacuum during a time interval of 1/299 792 458 of a second"... Huh? Isn't that circular reasoning?
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- Wouter Vanbelleghem (age 36)
Antwerp, Belgium
A:

Your question gets at a key issue. The only quantities to which we can assign non-arbitrary values are dimensionless ones, such as the ratio of a proton mass to an electron mass. Any quantity with units can acquire a different value just by redefining the units. So the real question becomes whether various dimensionless quantities that involve c have changed over time. Perhaps the most familiar such quantity is the fine structure constant, 2πe2/hc. So far as anybody can tell from looking at the spectral lines from ancient galaxies, it hasn't changed.

Of course, you might argue that just means h and e have changed in a way to compensate for the change in c. Unless some other dimensionless quantity has been found to change, adding such hypotheses just makes things complicated without getting anywhere. If it does turn out that some fundamental dimensionless quantity has changed, then attributing the change to change in c may be one option.

Mike W.

p.s. I think the discussion earlier in the thread was more about whether c is constant as viewed in different frames, not as viewed over time.

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(published on 08/21/2013)

Follow-Up #23: Wikibooks on relativity

Q:
Hi, Modern relativity is the proposal that the laws of physics are due to symmetries. An immediate consequence of this is that a pseudo-Riemannian, four dimensional manifold is required for the physical laws that we observe. Such a manifold has a constant, 'c', that relates spatial and temporal measures. Check out Wikibook's Special Relativity which has an entire section on why the speed of light is constant in modern relativity theory.
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- John (age 100)
Confederacy
A:

A quick look at that section indicates that it derives the general form of the Lorentz transforms, including the constancy of light speed, from the assumptions of symmetry and  that there is no relevant material background for the light propagation. I do not see in this argument any proof that c couldn't be infinite, which would return us to Galilean relativity. Of course, in our world we have Maxwell's equations, finite c, and Einstein's relativity.

Mike W.

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(published on 09/02/2013)

Follow-Up #24: Does light lose energy as it travels?

Q:
How can a photon travel for billion of years with the same speed, without losing enery? What is the source of energy for photons?
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- Zacki (age 23)
Mumbai, India
A:

Hi Zacki,

Let me turn your question around: in a vacuum, why would a photon lose energy? Even a baseball in space won't lose much energy, since there isn't any air resistance, friction, etc. The baseball will interact with radiation pressure, however, so it might lose energy slowly over thousands of years.

Photons, however, don't interact strongly with anything except charged particles. When they travel through empty space, one might expect that there is no mechanism by which they can lose energy.

Actually, however, there is one way that photons do lose energy as they travel through space. Because the universe is expanding, the photon's wavelength increases very slightly over time, and in so doing loses a bit of energy.

For the record, the source of a photon's energy is the "flashlight." For example, accelerating charges, hot objects, and particle decays can all lose energy by radiating photons. These photons are simply packets of electromagnetic energy.

David

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(published on 04/16/2013)

Follow-Up #25: theorems in physics

Q:
Fantastic Q&A! I am seeking clarification on the following: "In physics, we don't prove theories to be right, but we do prove theorems about the math used to hold together our theories". Can you please clarify what you mean by "prove theorems about the math"? Are there many examples where the math is correct (valid), but the truth it points to is invalid? An example that comes to mind is trying to apply classical physics at the quantum level. I just want to make sure I'm on the right track.
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- Darcy (age 32)
Toronto, ON, Canada
A:

You're on exactly the right track. The example you raised is a particularly important one. John Bell proved some theorems about how any system that obeys some of our basic intuitive assumptions must behave. All of classical physics would obey those assumptions. Our actual world violates the conclusions, Bell's Inequalities. So the theorem is useful because it tells us that at least one of those assumptions doesn't apply to our world.

Emmy Noether's Theorem is another famous one. She proved that for any continuous symmetry of the physical laws there's a corresponding conserved quantity. For example, if the laws are the same as viewed from any direction, then angular momentum must be conserved. The theorem by itself ties together parts of our understanding of the world, but the theorem by itself doesn't guarantee that the assumptions have to be true.

There are many other useful theorems, but they all have the same if-then form.

Mike W.

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(published on 05/31/2014)

Follow-Up #26: circling at the speed of light

Q:
I found this Q&A which is wonderful, by the way, thank you! by Googling Why is the speed of light the speed that it is? In other words, we can explain pretty thoroughly why a car is traveling at 60mph at a specific moment in time. Is there a comparable explanation or even a speculation or two as to why EM waves travel at ~300x10^6 m/s in a vacuum? (This discussion circles the question but Im not seeing a direct response. If its here and Ive overlooked it, I apologize.)
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- Roberta Lord (age 62)
Albuquerque, NM
A:

Unfortunately, we can only continue to circle the question. If you didn't know the speed of light, you could figure it out by making some measurements of electromagnetic effects, such as the amount of volatge induced on a coil when the magnetic field in it changes. Maxwell had those coefficients in his equations, which do correctly predict the speed of electromagnetic waves. We have, however, no deeper theory to give us the values of those coefficients in Maxwell's equations.

Mike W.

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(published on 07/06/2014)

Follow-Up #27: More on special relativity

Q:
Light moving at a constant speed is still perplexing to me. I have read your answers and it is not so much that the whole invariance is counter-intuitive as it is the repercussions that confuse me. I am ready to accept the fact that "that's just how the universe works" but I wish to understand the results a bit further. I read an article that said even moving frames are irrelevant. Does this mean that if I approach light as it approaches me, from my perspective the light would still only come at the speed of light. I understand the whole Doppler effect but light does take time to move and therefore by being in a reference frame moving towards it, you should perceive the light approaching you at a speed greater. The reverse being if I shot off a beam of light while moving in the same direction, would the light no be perceived from my perspective moving at a speed of c-v. If so maybe I just misunderstood the "any frame of reference" part.
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- David (age 18)
Indiana
A:

"Does this mean that if I approach light as it approaches me, from my perspective the light would still only come at the speed of light. " Yes.

" by being in a reference frame moving towards it, you should perceive the light approaching you at a speed greater. " You asume that the words "in a reference frame moving towards it" have meaning. It turns out that they don't. Each reference frame is at rest with respect to itself. Some other frames have it moving away from that light, some have it moving toward the light. All those reference frames have light moving at c with respect to themselves.

 

If you try to take apart your intuition, which says otherwise, into components you will find some deeper intuitions.

"1. Time intervals are plain facts, not dependent on reference frame.
2. DIstances are plain facts, not dependent on reference frames."

Although both of these intuitions work well enough for common experience, they both are simply false.

Mike W.

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(published on 08/05/2014)

Follow-Up #28: relative velocity of light source

Q:
The last answer - that whether or not an observer is moving towards a source of light is frame dependant - would seem to conflict with astronomical observations, where red-shift & sometimes blue-shift is routinely used to determine the relative motion of stars in a galaxy, or the 'local motions' of galaxies in a cluster. If I'm moving towards a distant star I will observe a blue-shift but you seem to suggest that another observer approaching the star at a faster speed, will perceive me as moving away from it as I will be moving outward relative to him. But surely, since he would simply observe a greater blue shift, such an assumption (that I'm moving outward) would be wholly unjustified !? Does not the blue-shift (or red-shift) give an unambiguous indication of motion towards (or away from) a source of light ?
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- Rick Crawford (age 36)
London, England
A:

All special-relativistic frames agree on whether you and the light source are getting closer of farther. Say you're getting closer, so you see blue-shifted light.  You say the source is moving toward you. The source says you're moving toward it. Somebody else can say you're moving away from the source, but not as fast as it's moving toward you.

Mike W. 

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(published on 09/26/2014)

Follow-Up #29: Why is light special?

Q:
I've read every question on this page and every answer so I'm sorry for being redundant, but simply put, I don't understand why light is so special that certain laws don't apply to it, making it so absolute. Since light has mass, couldnt someone technically "push" the light or transfer its momentum onto the light making it go faster? In addition, when light is pulled into something by gravity such as a black hole, wouldn't this "pull" of gravity cause the light to accelerate or speed up?
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- David sherman (age 12)
New Jersey
A:

In some ways it's unfortunate that we can sense light, a zero-rest-mass wave. Because of that, we call the universal speed limit, c, the special speed that appears in all the rules for translating coordinates from one frame to another, "the speed of light". The basic rules would be the same even if there were no light or other massless (meaning no rest mass) particles traveling at c. 

Particles fall into two categories, ones with rest mass and ones without rest mass. Light is in the second category, along with gluons and (we assume) gravitons. Particles in that category all travel at speed c. Particles with rest mass always travel at less than c.

So light doesn't break any rules, it follows the same rule book as all the other particles. It's just part of the minority of types that happen to follow the rules for zero rest mass.

With regard to acceleration, we've also addressed that question in other threads, e.g. .

Mike W.

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(published on 12/03/2014)

Follow-Up #30: What's my velocity?

Q:
Thanks for all the answers, and the questions too, I've learned a lot! Now I found myself a maybe rather dumb question: how do we find our speed without a reference? E.g. My infinite fuelled spaceship keeps accelerating, how can I tell if I have been close to, or at, or even over the speed of light?
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- Vince (age 33)
Australia
A:

Vince- Your question does a great job of capturing the collision between our intuitions an special relativity. The bottom line of the answer will be that it is completely meaningless to say what speed you are traveling at, i.e. if the current laws of physics are correct nothing can give any answer to that question. (For related questions see:  .)

Let's say that you set up a Michelson-Morley experiment in your ship to measure your velocity with respect to some medium in which the speed of light is equal in all directions. Ignoring your acceleration, you find that experimental the result is always what Michelson and Morley found: zero. The speed of light is uniform for observers in all those different states of motion. Any one of them can be called the state of rest, equally consistently with all the laws of physics.

Of course, if you have a favorite frame (say the frame in which the cosmic microwave background is uniform) you can always measure your velocity with respect to that frame by looking outside and measuring it. The answer you obtain will always be less than c.

Now what about acceleration? It turns out that the sorts of acceleration that might occur due to gravity as you go by stars etc. also don't affect any of your measurements in the ship. The measurements are affected by any acceleration caused by your engines firing, however. While the engines are firing you will find that clocks at the front of the ship run a little faster than ones at the rear. The accumulated time difference can be used to tell how much the velocity has changed from its initial value due to the rockets firing. (For simplicity here I'm assuming that the acceleration is always forward.)

Mike W.

 

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(published on 12/07/2014)

Follow-Up #31: adding velocities relativistically

Q:
hi, i have read over all the questions so far and was wondering about a possible loophole in the logic, lets say for example that you are in a frame of reference(frame A) and you are watching a passing particle (B) wave moving to the "left" at 2/3 C. Now, you also see a second particle moving in a parallel path to the "right". if both particles pass each other at more than half but less than the speed of light ( which is entirely possible for both particles alone), then from the observer wouldn't the particles pass at 4/3 c, faster than light?
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- Will L. (age 15)
A:

Certainly, (4/3)c is their relative velocity in your frame. In either of their frames, however, the relative velocity has magnitude (12/13)c. Nobody sees any object moving past themselves at speed greater than c. 

Mike W.

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(published on 02/11/2015)

Follow-Up #32: understanding relativity: velocity and momentum

Q:
Firstly, thank you very much for all the information in this thread, it is hugely useful. The one question I keep coming back to is: do I just have to accept that the speed of light is constant (irrespective of the position or speed of the observer) or is there a way of better understanding it? To try and make myself clearer, what I am really wondering is whether there is something special about the speed of light that doesn't apply at all to speeds close to the speed of light. For example, take a light pulse sent from a particular point in a particular direction and a bullet fired from the same place at the same time with a speed very close to c (say a mere 1m per second less (theoretically possible)). If I am a stationary observer at the same point, I think I see the light pulse moving at c and the bullet moving 1m/s slower. Then I get in a (very fast) car moving in the same direction as the pulse and the bullet, at the same speed as the bullet. I believe that from my new frame the bullet is stationary, but the light pulse would still be moving at c. This is where my noodle gets fried! I think the only thing to say is that anything moving at light speed essentially lives outside of and independent to any frame of reference hence always moves at c relative to the observer (whereas the bullet, at less than light speed, is within my frame of reference). It is the behavioural difference between something going at nearly light speed and light speed that I struggle with - though I expect the answer here is that it's a non-linear relationship and 1 m/s slower than c is actually a long way from light speed (i.e. the amount of energy required to get closer to c is enormous, actually infinite hence impossible). If this is the case then I am back to my original point which is that I just have to accept the "special" property of light speed and it doesn't really make sense to compare it to something going a "little bit" slower (because there is really no such thing as a little bit slower than light speed).
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- Richard (age 41)
London, UK
A:

Your understanding is correct. If you want to make sense that there's something non-linear that grows as v--> c, you could look at the momentum, p=m0v/(1-(v2/c2))1/2. That looks like v for v << c  but is indeed infinitely far from the v=c case whenever v < c. This graph shows quantitatively how p/mgrows as v/c grows. Notice that for v/c = 0.9, p is already about twice what you might have expected, and then it really takes off for larger v/c.

Mike W.

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(published on 04/05/2015)

Follow-Up #33: A thank you

Q:
Not a question. Just want to express my gratitude and admiration for the time and effort put to clarify so many interesting questions about an even more interesting topic.You, Sir (s), are a trully "c" in this Q&A.
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- Severina (age 33)
Joao Pessoa, Brazil
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.

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(published on 04/11/2015)

Follow-Up #34: Doppler shifts and speed

Q:
What is the relationship between Doppler effect and light speed? I mean, if light speed is the same respect to any observer, why does Doppler effect allow us to determine the approaching or receding of the celestial bodies (or the so-called redshift or blueshift)?
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- Daniel (age 26)
Medellin, Colombia
A:

The Doppler effect shows up as a change in the frequency of the light, not the speed. Star light has some sharply defined "lines" at specific frequencies corresponding to energy differences between states of common atoms. Shifts in the frequencies of those lines tell us whether another star is moving toward us or away from us and how fast.

Mike W.

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(published on 04/19/2015)

Follow-Up #35: why our particular speed of light?

Q:
I missed the answer to "Why" light travels at 299,792,458 m/s and not 1,000,000 m/s or some other figure? I understand that the speed of light isn't constant depending on circumstances.
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- Carl (age 57)
Ontario
A:

The speed of light is constant, as measured locally in a vacuum. The lower speed measured in say glass or water is the speed of light dressed in some excitations of the medium, a different thing. The pure physical constant is the same everywhere.

So why does it have the particular value that we find? Our non-answer is here: http://van.physics.illinois.edu/QA/listing.php?id=17242.

Mike W.

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(published on 07/03/2015)

Follow-Up #36: relativity and lifetimes

Q:
Hello and congrats for your awesome job with this Q&A. We live in a quasi-Euclidean works so it's very hard for us to think in a different way. You need education and a lot of empty "space" in your brain. The great majority of us just can't understand why a clock would be slower on a lower relative speed: " if I travel faster will I live longer?" That's the question the layman asks. I have no idea if living beings live "relatively" or "absolutely" or even if this question makes sense. Maybe you can help me out. Anyway, if speed can make distance "smaller" (in time terms) why is so difficult to understand that speed makes time "smaller" provided that distance is the same?
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- Luis (age 45)
Lisbon, Portugal
A:

That question captures nicely just what many people wonder about. (a follow-up to  , which was getting too long)

In most senses, someone's perceived lifetime is fixed regardless of their gravitational position and state of motion. That's because all the local clocks stay synchronized. That includes your heartbeat, your watch, the gradual aging of your cells, your metabolism and need to eat, ....  There could be some senses, however,  in which you live a different amount depending on those relativistic effects. Say that your only real goal in life is to watch the World Cup. For you the rest (eating, sleeping,...) is just empty filler.  Going off on a fast-moving spaceship and then returning would not increase your expected number of heartbeats but it would affect how many World Cups you'd be able to see in your lifetime. That's because the WC runs on Earth time, not your local heartbeat-watch time.

Mike W.

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(published on 07/04/2015)

Follow-Up #37: does falling light accelerate?

Q:
I understand light is bent around a black hole. It seems to be in a similar fashion as an object passing through a planet or stars gravitational field. I'm just making an observation that a black hole seems to exert a force on light as it bends around the singularity. What happens to the light that falls directly into the singularity? Logically, the same force would get exerted on the light and the light would accelerate beyond "c". However, I understand "c" doesn't change, so what happens in this sticky situation?
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- Kyle (age 17)
CA
A:

Other than the part about the singularity, your question applies to light "falling" toward any mass, including the Earth or the Sun. It seems as if it should accelerate, yet according to any observer close to the light, it's still traveling at c. That's assuming the observer uses the same standard definition of c in terms of local clocks and local metersticks. The problem is that the gravity from that mass affects the clocks and metersticks. For example, observers far from the mass think that the clocks near the mass are running slow. In General Relativity gravity shows up through these sorts of distortions of spacetime, not through local changes of c.

Mike W.

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(published on 09/17/2015)

Follow-up on this answer.