# Why Constant Speed of Light

*Most recent answer: 10/22/2007*

- Bill (age 16)

vancouver, BC, Canada

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.

*(published on 10/22/2007)*

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

- Bill (age 16)

Vancouver, BC, Canada

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

*(published on 10/22/2007)*

## Follow-Up #2: light near a black hole

- Bill (age 16)

Vancouver, BC, Canada

^{2}) 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.

*(published on 10/22/2007)*

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

- Ganesh

Bangalore,Karnataka, India

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

*(published on 01/02/2010)*

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

- Ganesh

Bangalore,Karnataka,India

Mike W.

*(published on 01/02/2010)*

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

- Craig (age 20)

Kelowna, B.C. Canada

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.

*(published on 03/09/2011)*

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

- syd

Hyderabad,Andhrapradesh,India

Mike W.

*(published on 07/28/2011)*

## Follow-Up #7: Does light have mass?

- LEGO (age 50)

solon

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.

*(published on 12/17/2011)*

## Follow-Up #8: different concepts of mass

- LEGO (age 50)

Solon, OH, USA

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.

*(published on 12/25/2011)*

## Follow-Up #9: deriving speed of light?

- Jeff (age 52)

Clovis, NM, USA

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.

*(published on 03/17/2012)*

## Follow-Up #10: thanks

- Aaron Von Gauss (age 38)

Boynton Beach, FL

Mike W.

*(published on 11/01/2012)*

## Follow-Up #11: philosophy of relativity

- Michael J. Schreck (age 51)

Danbury, CT, USA

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.

*(published on 12/24/2012)*

## Follow-Up #12: fundamentals about light and relativity

- Amarpal Singh (age 38)

Thousand Oaks, CA, USA

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.

*(published on 01/20/2013)*

## Follow-Up #13: pressure causing gravity in relativity

- Bassem (age 18)

ramboland

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.

*(published on 02/05/2013)*

## Follow-Up #14: questions about light reflection

- Ricky (age 57)

Huntsville AL 35803

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.

*(published on 03/04/2013)*

## Follow-Up #15: Does light lose energy as it travels?

- Zacki (age 23)

Mumbai, India

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

*(published on 04/16/2013)*

## Follow-Up #16: Is the speed of light zero?

- Taeke van der Sluis (age 42)

Netherlands

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.

*(published on 07/05/2013)*

## Follow-Up #17: light beams crossing

- Taeke van der Sluis (age 42)

Netherlands

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.

*(published on 07/08/2013)*

## Follow-Up #18: philosophy and physics

- cesar (age 30)

France

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

Mike W.

*(published on 07/17/2013)*

## Follow-Up #19: speed of reflecting photons

- Don (age 60)

Arkansas

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.

*(published on 07/18/2013)*

## Follow-Up #20: Is the speed of light constant in all directions?

- John Dees (age 55)

Ferriday, LA USA

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

*(published on 07/18/2013)*

## Follow-Up #21: reflecting photon velocity

- Don (age 60)

Arkansas

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.

*(published on 07/19/2013)*

## Follow-Up #22: can you determine your absolute speed?

- Kyle (age 21)

St. Albert, AB, Canada

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.

*(published on 08/18/2013)*

## Follow-Up #23: Does the speed of light change?

- Wouter Vanbelleghem (age 36)

Antwerp, Belgium

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, *2πe ^{2}/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.

*(published on 08/21/2013)*

## Follow-Up #24: Wikibooks on relativity

- John (age 100)

Confederacy

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.

*(published on 09/02/2013)*

## Follow-Up #25: theorems in physics

- Darcy (age 32)

Toronto, ON, Canada

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.

*(published on 05/31/2014)*

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

- Roberta Lord (age 62)

Albuquerque, NM

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.

*(published on 07/06/2014)*

## Follow-Up #27: More on special relativity

- David (age 18)

Indiana

"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.

*(published on 08/05/2014)*

## Follow-Up #28: relative velocity of light source

- Rick Crawford (age 36)

London, England

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.

*(published on 09/26/2014)*

## Follow-Up #29: Why is light special?

- David sherman (age 12)

New Jersey

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.

*(published on 12/03/2014)*

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

- Vince (age 33)

Australia

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.

*(published on 12/07/2014)*

## Follow-Up #31: adding velocities relativistically

- Will L. (age 15)

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.

*(published on 02/11/2015)*

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

- Richard (age 41)

London, UK

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=m_{0}v/(1-(v^{2}/c^{2}))^{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/m_{0 }grows 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.

*(published on 04/05/2015)*

## Follow-Up #33: A thank you

- Severina (age 33)

Joao Pessoa, Brazil

.

*(published on 04/11/2015)*

## Follow-Up #34: Doppler shifts and speed

- Daniel (age 26)

Medellin, Colombia

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.

*(published on 04/19/2015)*

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

- Carl (age 57)

Ontario

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.

*(published on 07/03/2015)*

## Follow-Up #36: relativity and lifetimes

- Luis (age 45)

Lisbon, Portugal

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.

*(published on 07/04/2015)*

## Follow-Up #37: does falling light accelerate?

- Kyle (age 17)

CA

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.

*(published on 09/17/2015)*

## Follow-Up #38: photons in expanding space

- Manohar DC (age 36)

Bangalore, Karnataka, India

The photon in an expanding space doesn't actually emit another photon as its energy goes down. Energy conservation in General Relativity is a lot messier than in simpler spacetime pictures, e.g. Newtonian or Special Relativistic. The issue is over my head, but I'm told that the missing energy can be assigned to a growing gravitational potential energy of the whole expanding spacetime. See:http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html

http://math.ucr.edu/home/baez/physics/Relativity/GR/energy_gr.html

Time is relative but you can ask simple physical questions that give a non-arbitrary age. Take some sort of well-defined object, such as a hydrogen atom. There's a frequency to the light it emits and absorbs. You could ask how many of those wave periods have elapsed for an atom not subjected to any major forces since it was born.

Actually, that only works back to the time when H atoms formed. To go back further you'd pick modes of nuclear particles to bridge the time between when they formed and when atoms formed. Then you'd pick pther processes to step back before that. You can put together an operationally well-defined age. Using particles that did not get pushed around by non-gravitational forces gives us an operationally well-defined way to pick a reference frame.

Mike W.

*(published on 10/08/2017)*

## Follow-Up #39: basic weirdnesses

- David Ashley Poole (age 73)

Annapolis, MD, USA

Some of these aren't so hard to get used to and some remain dizzying. The constant speed of light and the more general unfamiliarity of spacetime geometry gets more acceptable. Our intuitions are just based on little pieces of experience, so it shouldn't be too hard to accept that we get intuitions that only work for those little pieces. They're sort of like our intuition that tells us the Earth is flat.

As for the "particle/wave duality", when you get further into it that particular difficulty dissolves. It's replaced by even more basic issues, like the entanglement question you mention and the related "measurement" problem. If there's a way of making sense of our quantum world, I don't know it.

I'm not quite sure what the issues are with your point 4.

Mike W.

*(published on 01/19/2018)*

## Follow-Up #40: holography

- Chris (age 34)

Qld, Australia

You're conflating two different ideas. One is holography, the idea that all the events we describe as part of a 3D +time world have an exactly mathematically equivalent description as a 2D+time world with different specific laws. The other is the idea that we all exist as part of a simulation run by some intelligent beings following a different set of laws than the ones in the simulation. The second idea is not really part of physics, so I won't comment on it except to say that personallly I don't like the idea.

As for holography, that's a really interesting idea although the math is over my head. There would be nothing illusionary about our usual 3D description, it would just be the mathematical description more accessible to our limited evolved brains. Presumably the description in the 2D math would not have the simple large-scale physical properties that our intuitions can handle.

Whether or not string theory ever works out, the motivation for it is not merely decorative. Right now there's no consistent overall theory- combining general relativity and quantum mechanics leads to crazy results. There are also some obvious holes in our understanding. We don't know what's going on with either dark matter or dark energy. Traditionally, contradictions and gaps have been solved by finding deeper theories. So that's the motivation.

Mike W.

*(published on 04/03/2018)*

## Follow-Up #41: holographic principle in a deSitter universe

- Kartik (age Tc)

Michigan, USA

I asked a more knowledgable colleague (Philip Phillips), who said that the extension of the holographic principle to our universe was conjecture. I wish I knew enough to help out more.

Mike W.

*(published on 12/20/2018)*

## Still Curious?

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