Of Particular Significance

The First Principle of Relativity

Matt Strassler 11/27/2011

The principle of relativity comes up regularly in the context of space travel, and this week’s launch of NASA’s “Curiosity” rover mission was no exception.  The BBC has a pretty nice article about it, but as happens so often in press articles, it stumbles in a big way at one point.  Quoting from the article: “By the time the encapsulated rover was ejected on a path to the Red Planet, it was moving at 10 km/s (6 miles per second.)

Oh my heavens.  10 kilometers per second.  That sounds very fast; highway speeds are 100 kilometers per hour.

But the statement is completely meaningless.

In fact, right now, as you sit in your chair, reading this nice little article, you are moving at 30 kilometers per second.  In a sense, anyway.  Yet nobody is about to issue you a traffic ticket, or give you an award for traveling faster than a speeding bullet (less than a kilometer per second.)

Do you know that Einstein did not invent the principle of relativity?  The original principle of relativity — which includes the statements that the laws of nature do not permit you to determine if you are stationary, and thus your speed (and that of anything else) always has to be stated as relative to another object — goes back at least to Galileo, who is credited by scientists as having formulated the relativity principle. Einstein modified the details of this principle, in a striking and radical way, but without discarding Galileo’s basic realization that all speeds have to be measured as those of two objects relative to one another.

Galileo recognized that if you are on a ship sailing in calm waters, and you are inside your windowless cabin, there is nothing you can do to tell how fast the ship is moving.  If you are able to toss a ball back and forth with a friend when you’re on shore, you will be able to throw and catch the ball just as easily if the ship is moving at five kilometers per hour, or fifteen, through the water — as long as it is moving in a straight line and not being jostled by wind or wave.  An extreme version of this is that you can easily toss a ball back and forth on a jet plane moving at hundreds of kilometers per hour, as long as the ride isn’t turbulent.  (I’m not sure you should try this in the aisles, but you might try jumping up and down, as I did when I was nine years old to see what would happen; you’ll find it feels exactly the same as when you’re on the ground.)  And it’s a good thing!!  If Galileo’s relativity principle weren’t true, we’d have a tough time eating, drinking, and walking on airplanes; the fasten seat belt sign would be on all flight!

What does the speedometer in a car actually measure? It measures the speed of the car relative to the ground.  Of course, if you are traveling by car, that’s typically the only relevant speed — you want to know how long it will take to get from your starting point to your destination, and since the two locations are stationary relative to the ground, the speed of the car tells you how long it will take to travel between them.

But for an airplane, there are two measures of speed that matter.  One of them is “ground speed”, and the other is “air speed”.  Ground speed determines how quickly you are covering the distance between your point of departure and your point of arrival.  Air speed, however, measures how quickly the air is flowing over the wings of the plane.  It is air speed that determines how and whether the plane flies.  Also, the maximum speed of a plane is a maximum air speed, not a maximum ground speed, because the engines have to work against wind resistance, which depends on air speed only.

If there were no wind, then the air and the ground would both spin around the earth’s axis exactly once each day, and ground and air speed would be identical.  But the atmosphere does have strong winds, so air and ground speed can be quite different.  In the mid-latitudes where most of us in North America and Europe and much of Asia live (as well as in southern South America, southern Africa and Australia) the winds at jet altitudes blow west to east.  Much of this air flow occurs in the “jet stream”, which is up at the altitudes where planes fly.  This “river” of air can move at roughly 100 to 250 kilometers per hour (roughly 50 to 150 miles per hour) relative to the ground. And what that means, in turn, is that a plane with an air speed of 800 kilometers per hour may have a ground speed of perhaps 700 kilometers per hour if it is traveling to the west, and perhaps 900 kilometers per hour if it is traveling to the east.  This in turn explains (roughly) why a flight from Europe to the United States can take as much as a couple of hours longer than a flight from the United States to Europe; the plane’s air speed is the same in the two cases, but its ground speed is not.  (The same principle makes a boat trip longer when you are traveling up a river, against the current, than when traveling down the river; the boat’s engine allows it to travel at a fixed speed relative to the water, and this is not the same speed relative to the shore for up- and down-river travel.)

Of course, when you’re in the plane (or boat), you don’t feel any speed at all; it’s the same to you if the air speed is 800 kilometers per hour or 500, because you and the plane (and the air inside the plane) are stationary relative to one another.  In other words, you don’t have a speed.  You have speeds, plural, relative to other things, plural: these include speed relative to the plane (zero), speed relative to the outside air (800 kilometers per hour) and speed relative to the ground (faster or slower than air speed depending on where you are going.)  Which version of your speed is better?  Well, that depends on what you want to know; ground speed is relevant for travel time, air speed is important for the integrity and flight characteristics of the plane, and plane speed is relevant to how long it will take you to get to the lavatory from your seat.

What about for a spacecraft?   The new spacecraft with the Curiosity rover in it is traveling from Earth to Mars.  It has a speed relative to the Earth.  It has a different speed relative to Mars.  It has a different speed altogether relative to the sun.  Which one is relevant for the time of travel?  None of them!  An airplane’s starting and ending point are at a fixed distance from one another, but our spacecraft has a trickier problem, because Mars and Earth are moving relative to one another.  And they will move a great deal relative to one another during the eighteen-month voyage of the spacecraft!   Speed is not a simple thing in space, where everything is moving relative to everything else.  That’s one of many reasons why rocket science does indeed take some serious training!

An aside for the future: In fact, because the earth is round and spinning, even a plane’s ground speed and air speed can get tricky if you think too hard about it.  On top of that, planes don’t always take the shortest ground route when they fly, since sometimes they can ride a flow of air on a longer ground route to help them get a shorter flight time.  The motions of planets and spacecraft, which travel in looping orbits around the sun, are complicated too.  So if we go any deeper into this subject we’re going to have to go a lot deeper.  But all that’s relevant here is that for short enough times all the motions are close enough to straight lines, and that allows us to appeal to Galileo’s principle of relativity. Let’s step back from the brink of this very long discussion for now, because there are other issues to deal with.

This brings us back to you, sitting in your chair.  You may feel immobile, but you’re not.  First, the earth is carrying you as it spins round its axis at something like 1000 kilometers per hour, depending on your latitude.  Still more dramatically, the earth is also traveling around the sun, and we are all carried along with the earth — at about 30 kilometers per second relative to the sun.  You don’t feel it, for two reasons.  First, you only feel what you touch, and obviously you aren’t in contact with the sun.  You’re in contact with your chair, and with the air in the room, and since you’re stationary with respect to them, you feel no motion.  And second, your motion is in almost a straight line (it isn’t straight, but it bends very slowly)  so Galileo’s principle of relativity applies to you, your chair and your room.

Meanwhile, the sun orbits the center of our  galaxy — the Milky Way, that great city of stars in whose suburbs we live — at a speed of 220 kilometers per second.  Whither thou goest, I will go — the earth travels with the sun, so our own speed relative to the galactic center is of a similar size.  And the galaxy moves relative to other galaxies at even higher speeds… none of which we feel.

Finally, back to the BBC article.  The spacecraft is traveling, according to the BBC, at 10 kilometers per second.  Relative to what?  I would guess that the speed quoted is probably the speed of the craft relative to Earth.  But the article needs to say so!  Otherwise the statement has no content.  In fact, since Mars is further from the sun, and travels more slowly in its orbit than Earth (about 24 kilometers per second relative to the sun) it is quite possible that the spacecraft, despite having fired its rockets, has actually slowed down relative to the sun!  That is, though it started off, like the rest of the earth, moving at 30 kilometers per second relative to the sun, it may now be moving at a slower speed (from the sun’s point of view) in order to make it easier for the craft to match Mars’ orbital motion down the line. That would be interesting to know, but unfortunately the BBC was silent on the matter.

And if you were on the spacecraft?  Now that the rockets have stopped firing, and the spacecraft’s motion is steady, you would feel no motion at all.  In accordance with Galileo’s principle of relativity, you would not know which direction you were headed or how fast relative to any planet or star, unless you very carefully measured the changing positions of the planets in the sky and watched the sun become gradually smaller.  And were it not for your trust in the engineers and scientists who assured the rocket would send you in precisely the right speed and direction relative to Mars and Earth and the sun, you would have no idea whether you would someday approach Mars at all, or whether instead you would simply drift for eons as one more micro-planet among the multitudes.

44 Responses

  1. As redshift found its way into this thread I’m going to take the opportunity to ask some naïve questions.

    I am stationary, relative to the Earth. A photon is approaching me at “c”, and at the start of the scenario is one light minute away.

    I accelerate away from the photon at an appreciable % of “c”.
    The photon is still closing the distance between us at “c”, but it is redshifted. That means that when it catches up with me I will measure a red-shift.

    Does the photon have less energy as a result of being redshifted?
    How could my action take energy from a photon that was up to one light minute away?
    Is it only my measurement of the energy of the photon that is different?
    Is it equivalent to a situation in which if I am in a car travelling at 20mph and am hit from behind by a car travelling at 30mph, it hits me with less energy than if I had been stationary, but I didn’t actually take any energy from the second car by driving my own?

    Am I rambling? 🙂

  2. Matt, I was fascinated by your comments about whether or not photons “experience” time/distance.

    My understanding of this was:
    Taking the time dilation equation to its ultimate conclusion may seem a logical thing to do, but it is not supported by special relativity because of the lack of mass of the photon which puts it outside the remit of special relativity. It seems that the best we can say is that we have no way of knowing if photons experience time, or not. Nor do we have any scientifically accredited theory that covers this, nor any way to test the idea experimentally, as no massive object can reach the speed of light, and a clock cannot be fixed to a photon.

    I’ve never really been happy with this, but have yet to find a satisfactory counter.

  3. Sorry if this is a very basic question because I have very little knowledge or understanding on the subject but are we not travelling at the speed of light relative to the photons?

  4. I’m hand-waving here, because I don’t have any precise numbers. But I do know that one of the (several) ways that NASA tracks interplanetary probes is by putting a ping signal onto a transmission to the spacecraft, which the spacecraft is instructed to immediately retransmit back to Earth. The round-trip time is used to track the spacecraft’s position. The retransmission delay within the craft is measured to nanoseconds before the mission, and corrections are applied for similar delays within the Earth-side equipment, and even for atmospheric effects. This method has been used on a number of missions, but in particular on the Cassini mission to Saturn, with round-trip times on the order of hours and required accuracy on the order of kilometers. I’ve heard it stated (without proof) that this is actually the most accurate method of tracking the spacecraft (which surprised me, because I would have thought that keeping track of the speed via the Doppler effect would have been the most accurate).

    For what it’s worth …

    Oh, and BTW, a small correction to this article: Curiosity’s travel time to Mars is just over 8 months, not eighteen months.

  5. Since all experiments to date have been done within earth’s gravity well, is it possible that c would vary from the known standard if an experiment to measure it were done in deep space? Put simply, does the fact the most, if not all experiments probing the speed of light in a vacuum have taken place on or very near the earth matter?

    1. Unfortunately I’m not an expert on precision measurements of this type, so I do not actually know what are the best tests of this type. I will try to find out.

      But one thing that I know is that the GPS satellites are extremely precise instruments that depend very strongly on getting the speed of light correct. The GPS satellites are more than 5 1/2 times further from the center of the earth than are you or I, so they are much further outside earth’s gravity well than you and I are. (That is, the force of the earth’s gravity on those satellites is more than 25 times weaker than the force of gravity on you and me.) So that provides a precise test that the speed of light does not change even when you go much of the way out of the gravitational well of the earth. (Meanwhile the success of the GPS system tests other aspects of special and general relativity too.)

      If any readers know of even more powerful tests that the speed of light is the same far out in space as it is on earth, please let me know. And if you can put numbers on how precise these tests are, that would be great also. I suspect there are some tricks that employ bouncing laser light off a mirror that some astronauts placed on the moon, but again, I’m not the expert…

      Essentially what you’re asking is whether general relativity (Einstein’s theory of gravity) is correct, because general relativity would predict that the speed of light, measured by any observer as the light passes her or him, does not depend on the local gravitational field. There are many more tests of Einstein’s equations for gravity than there were when I was a graduate student, and there are more being made over time. So far, general relativity has passed all the tests, and though it is constrained far less well than special relativity, I doubt there is much room any more, given what we know, for a speed of light that changes significantly out in space compared to on the earth’s surface.

  6. I’m a CS Engineer from Spain. I’ve always found amazing physics and its implications but my knowledge of physics is not deep into the math so forgive my misunderstandings. I discovered recently your blog and have read many articles from it since then. I wish you could enlighten me or at least prove me wrong in my assertions.

    One of the things I find really interesting is the implications of causality for photons as they travel precisely at the speed of light. It’s my understanding of special relativity that the faster you go with respect to a set of events, those events seem to you to happen in a shorter period of time from your point of view. So when you go at precisely the speed of light, everything is happening at the same time.

    Also, the faster you go, not only events seem to happen in a shorter period of time but things shrink. And again, from a photon’s point of view (POV), not only everything happens at the same time but everything is infinitely small and this it has not moved. When a photon comes from the Sun it takes some 9 minutes to reach the Earth, but from the photon’s POV, zero seconds happened, so it had no time to move and in fact earth and sun are at the same spot. We could even twist this last thing a bit and further say that the photon is in all of the positions of its trajectory at the same time, from it’s POV, and that it just happens because from its POV all those positions are the same.

    So that makes photons really strange to me: they travel so fast that time and space do not seem to affect them (from their POV). And they are always traveling at the speed of light – only if they happen to collide with an atom they will disappear and their travel and existance will stop there.

    Photons are funny, I think it’s much more wise to worship the Sun than any other gods. Afterall, photons seem to be timeless, massless, and ubiquitous – but despite all that, we still can see them!

    1. 🙂 What this really tells you is that it would be tough to have a point of view if you were made from photons.

      It is not an accident that creatures that think do not travel at light speed! For indeed the experience of time and space is impossible for a massless object. If we try to imagine what a photon’s “point of view” would be, we’re really imagining endowing the photon with a little brain and sensory organs; but since there is no time for a massless object, no information would ever travel from its senses to its brain, and no processing would occur within its brain, even as it traveled across the universe. There is no possibility of psychological time, and therefore no observing or learning, for a massless object.

      Okay, I’m being a bit silly here — but what I am emphasizing is that the possibility of “point of view” does imply a certain level of consciousness that presupposes a sense of time. And that’s something that photons and other massless objects can’t have.

  7. Particle physicists (even yourself, I’m pretty sure) refer to neutrinos as traveling *close* to the speed of light. But according to the principle of relativity this is meaningless, right? Something is either going *at* the speed of light OR it has no meaningful (absolute) speed.

    So why do physicists always talk about neutrinos traveling close to the speed of light when you could just as easily argue that any particular one of them is at rest? I assume neutrinos are flying around the universe in all directions at all sorts of relative speeds, so is there some natural reference frame with respect to which particle physicists like to orient themselves when discussing neutrinos?

    1. Excellent question! Of course you are absolutely right that it does not make sense to say that neutrinos travel close to the speed of light without saying “relative to what”.

      So why do people so often say it? I try to avoid it — but the reason is that in practice it is true in almost any frame in which you will find yourself. Let’s see why.

      What are the physical processes that we know about where neutrinos are most often produced? They are produced in the sun’s fusion (with an energy, in the sun’s frame, of 0.1 to 1 MeV) [non-experts, recall 1 MeV = 0.001 GeV = 1 million eV] or in the decay of the neutron or other atomic nuclei (with an energy, in the neutron’s or nucleus’s frame, or order 0.001 to 1 MeV, though the energies have been indirectly inferred all the way down to 1 eV!!) or in supernovas or cosmic rays (with energies much larger than 1 MeV) or in muon decays (with energies of order 10’s of MeV’s.) Now suppose it is true (as is currently strongly suspected from cosmology) that all neutrinos have masses below 0.1 eV. Then any neutrino produced in one of these MeV-scale processes has a velocity, relative to the place where it was produced and relative to the earth and relative to the sun and relative to the galaxy, which is within a tiny fraction of the speed of light.

      One exception is that case I mentioned where you have an atomic nucleus (such as tritium) spitting off a very low-energy neutrino, along with a higher-energy electron. And that happens in only a tiny, tiny fraction of the tritium decays.

      So in realistic situations, no matter what you do, and no matter what frame you are in, you will find the neutrinos that are going by you have energies (as you measure them) that are much greater than their masses, and that guarantees of course that in your frame the velocities relative to you are very close to the speed of light.

      In short, it is certainly possible in principle to make neutrinos that travel well below the speed of light relative to any given frame, but in practice it is very difficult to actually do it!

      One more important exception are the neutrinos from the early universe, some of which are probably heavy enough relative to their effective temperature to be quite slow. But no one has ever figured out how to detect these neutrinos, so although their existence is plausible we are not in a position to study them in detail.

      There’s more to this story, but let’s leave it there for now.

  8. Andy said: “This situation might appear to violate relativity, but it doesn’t. You start with two relatively stationary items which share the same inertial reference frame. If you then move the detector, you are introducing energy to the system, and the detector will “feel” an acceleration. Since the energy was introduced at the detector, the dopplar shift is experienced immediately. However, if you instead accelerate the source, that increase in energy will take time to propagate to the detector.”
    I am always amazed at the ingenuity of relativists in defending relativity. Unfortunately this explanation by Andy has no basis whatsoever in special relativity. Einstein’s Principle of Relativity requires “perfect symmetry between inertial frames” (Rindler) i.e. that the same changed frequency be observed at the same time in each case, resulting in the same perceived Doppler shift for movement of the source and movement of the observer. This must be so otherwise the frames would be distinguishable contrary to the principle of relativity. I am yet to see a convincing explanation of why this situation is not an invalidation of the principle of relativity.

    1. Stephan; you are deeply confused. You made the detector move, or the source move, after being stationary; whichever one moved is no longer in an inertial frame and the symmetry is broken. See above.

      If you had made one of them move an infinite amount of time ago, then they would both be in inertial frames. But then your puzzle would be absent; the symmetry would be restored, and so would be the equivalence.

      I would encourage you to be less arrogant and more open to answers. You are trying to make sense of the words without understanding the equations; this easily leads to mistakes. It is not a matter of relativists being ingenious; it is a matter of using the equations correctly.

      1. Matt: Once again I disagree. Moving the detector (or the source) after being stationary does not mean it is no longer in an inertial frame as you claim. Providing it is now moving at a uniform speed it has simply moved from one inertial frame to another and the full theory of special relativity applies. Thus the principle of relativity requires “perfect symmetry between inertial frames” and therefore the same changed frequency must be observed at the same time for movement of either the source or the detector otherwise the two frames would be distinguishable contrary to the principle of relativity. The problem remains!

        1. Wow, a fundamental mistake: wrong usage of reference frames. When you say “If instead the source moves toward the stationary detector (at the same speed), a Doppler shift is only observed after a time delay which can be made arbitrarily large by increasing the initial distance between the source and the detector”, you do imply that the source has not been moved toward before. Thus, the two reference frames you choose are no longer “inertial” to apply special relativity. You must use general relativity here to analyze the whole process (over a period of time you choose).

      2. I’m really impressed that senior researchers do have mistakes with reference frames, just like I did in high school. Here is another example, in which people even file a patent on wrong calculation due to using reference frames improperly:

        That speedometer would reject the principle of relativity if it really worked.

  9. A question about Mars’ orbital velocity: In general, a higher orbital speed means a larger orbit. If you are in a roughly circular orbit and accelerate in the direction of motion (rather than in a single direction, which would mainly affect the orbit’s eccentricity), the radius of the orbit should increase. The angular velocity of the orbit may decrease (you may actually take longer to complete one orbit), but not your speed along the path of your orbit. So how is it that Mars’ orbital speed is 24 km/sec slower than Earth’s?

    1. [Edited by host] The speed required to maintain orbit is dependent on the mass of the object. Mars is smaller than the Earth. [Host: This is a classic freshman physics mistake, and it is wrong on many, many levels. The speed required to maintain orbit is independent of the mass of the object, as long as the object in question is orbiting another object that is much more massive than the first object. If this were not true: astronauts in the orbiting space station would not appear weightless; astronauts in space walks would immediately drift behind the space station; gravity could not be described as curvature of space and time as it is in general relativity; the orbit of the moon around the earth would not be roughly circular but would tend to lag behind the earth as it orbited the sun, and might even be pulled away from the earth altogether; etc. etc. etc.]

    2. I thought I’d answered this, but the comment reply disappeared somehow. Your intuition isn’t quite right, and you have to think about elliptical orbits versus circular ones, to see why.

      Before we do that, here’s something that’s easy to check. Remembering that the inward acceleration on an object in a circular orbit is v2/R, where v is the constant speed of the object and R is the radius of the orbit, the force required to keep an object in circular orbit of radius R and period T = perimeter/velocity = 2 π R / v is

      F = m a = m v2 / R = (2 π)2 m R / T2 inward

      If the force is provided by gravity from the sun, and the sun has mass M, then that force must also be equal to

      F = G m M / R2 inward

      where G is Newton’s constant. We need then only set these equal to find that objects orbiting the sun have

      m v2 / R = (2 π)2 m R / T2 = G m M / R2

      ⇒ v2 = G M / R and T2 = (2 π)2 R3 / G M


      (a) the speed of the orbiting object, and the period of the orbit, are independent of the mass m of the orbiting object

      (b) the speed falls like 1/R1/2, and the time of the orbit grows like R3/2 ; larger circular orbits have slower speeds and longer orbital times.

      Now the question is: what was wrong with your intuition. It is true that if you are in orbit and you fire your rocket in the direction that you are going, you will move toward larger radius — but you will also now be in an elliptical orbit. When you reach the maximum radius of the orbit that you are now in, you will be going slower than you were back in the original circular orbit you started in. Only when you reach the minimum radius of the orbit you are now in will you be going faster. Fire your rockets again to move yourself to move yourself to a circular orbit at the larger radius? You will again find that you initially speed up, but by the time you’ve made the orbit circular at the larger radius, you will be moving slower than you were in the original circular orbit. Rocket science is tricky.

      It seems strange that you could exert energy that would seem to want to speed you up and yet you would end up slower. The reason this works as it does is because moving to a larger-radius orbit costs gravitational energy (usually called gravitational potential energy, to distinguish it from kinetic energy, which is the more obvious energy due to motion), and this cost uses up all the energy that you expended using your rockets, and even more than that — leaving you with less motion-energy than you had in your orbit at the smaller radius.

  10. Correction:
    However by Einstein’s principle of relativity the two situations are equivalent since only relative motion is important and therefore there should be no difference between them contrary to what is observed.

    1. This situation might appear to violate relativity, but it doesn’t. You start with two relatively stationary items which share the same inertial reference frame. If you then move the detector, you are introducing energy to the system, and the detector will “feel” an acceleration. Since the energy was introduced at the detector, the dopplar shift is experienced immediately. However, if you instead accelerate the source, that increase in energy will take time to propagate to the detector.

  11. I wish to point out that while Galilean Relativity applies to mechanical systems, Einstein’s principle of relativity applies to all of physics including light, and not just mechanical systems. This is a major difference. While the former principle has been confirmed, the latter remains unconfirmed. A situation where the latter principle appears to fail is the following: Consider a light source stationary on the surface of the Earth and a stationary detector at some distance away from the source. If the detector moves toward the stationary source, a Doppler shift is immediately observed. If instead the source moves toward the stationary detector (at the same speed), a Doppler shift is only observed after a time delay which can be made arbitrarily large by increasing the initial distance between the source and the detector. However by Einstein’s principle of relativity the two situations are equivalent since only relative motion is important and therefore there should be no difference between them as is observed.

    1. Stephan: this is incorrect. You are confusing the source of the photons with the photons themselves. It is a classic mistake.

      If you move the source, the photons you are affecting are the ones being emitted by the source *now*. The ones that were emitted long ago are not affected by this motion. The detector will not see the effect until the photons reach the detector, which takes a light-travel time.

      If you move the detector, you are changing the detector relative to the photons that it is detecting — which were emitted by the source long ago.

      This is a nice example of one of the many classic mistakes people make in misunderstanding relativity. You have to pay very close attention to what Einstein’s equations do and do not say — otherwise you will get yourself profoundly confused.

      What Einstein’s equations say is that if you have a source moving toward the detector FOREVER it is the same as a detector moving toward the source FOREVER. If the source and detector are initially stationary and you CHANGE the situation, then you have to calculate much more carefully what the effect is.

      Incidentally particular mistake this has nothing to do with Einstein’s relativity. You can make the same mistake with Galilean relativity using sound waves.

      1. Matt: I disagree with you. Nothing in special relativity allows you to separate the light photons from the source in the manner you are suggesting. In deriving the Doppler and aberration formulas, Einstein wrote about “an observer …moving with velocity v relatively to an infinitely distant source of light”. No separation of light and source is considered. This is an interpretation introduced by you with no basis in the theory. The resulting formulas for Doppler frequency and aberration angle both involve the relative velocity v between the source and the observer. This leads to another problem for special relativity where the relative velocity between source and observer is involved and therefore which predicts many aberration angles for the differently moving stars in the same direction. However stellar aberration is observed to be the same for all stars in the same direction. This particular contradiction has been raised by physicists in the past. The explanations I have seen rely on ideas that are not part of special relativity and therefore not applicable.

  12. This gives me an opportunity to ask about something I’ve often wondered about – the dipole anisotropy in the cosmic microwave background. I’ve read that this implies that we’re “moving relative to the CMB” (although different websites give different speeds :/ ). Is this true? And does it imply some sort of absolute speed measurement?

    1. EXCELLENT QUESTION! This type of thing bothered the physicist Ernst Mach enormously, and his thinking about the matter was very influential on Einstein. Long but very interesting story, which I won’t try to remember here.

      This is related to the point that I can toss a ball just as easily inside a car running at 10 miles an hour relative to the ground as I can in a car running at 50 miles an hour. The laws of nature don’t care if I’m moving relative to something else: the only thing important for the tossing of the ball is that I, the car, and the ball (before I toss it) are all stationary, and the forces I need to exert to toss and catch the ball, the motion of the ball relative to me, the time it takes for the ball to fly up and return to my hand, etc., care not a whit for what the ground outside is doing. But it is still true that, on earth, the ground defines a natural frame of reference, relative to which we may choose to measure our speed. It is still a relative speed, however. And we don’t need to use it.

      The same is true for the cosmic microwave background radiation (CMB). Nothing we do in our daily lives are affected at all by what our speed is relative to the CMB. The forces we exert to toss a ball or send a rocket to Mars care not a whit for what the CMB is doing. It is still true, however, that, at least in our part of the universe, the CMB defines a natural frame of reference, relative to which we may choose to measure our speed. It is still a relative speed, however. And we don’t need to use it.

      So no, there is no absolute speed measurement even though we are moving relative to the CMB… just as there is no absolute speed measurement on the ground of the earth. You might say “wait — the CMB fills the whole universe!” It doesn’t matter. All that matters is that there is no experiment that you can do that will prove that the CMB is stationary and I am not, instead of the other way round.

  13. “Meanwhile, the sun orbits the center of our galaxy — the Milky Way, that great city of stars in whose suburbs we live — at a speed of 220 kilometers per hour.”

    I think you have a typo here. Solar system moves around the centre of our galaxy 220 km/sec not km/hour.

  14. @Sebastian

    Assuming the flight plan wasn’t modified, the spacecraft was launched with a C3 of ~11 km²/s² (see table 2 in http://trs-new.jpl.nasa.gov/dspace/bitstream/2014/41591/1/09-4690.pdf )

    C3 measures the remaining energy per unit mass once the spacecraft has “broke free” from Earth’s gravitational field (more details in Wikipedia: http://en.wikipedia.org/wiki/Characteristic_energy ) and this value of C3 is associated to a velocity of about 3 km/s with respect to the Earth in the next few days (weeks), before the influence of the Sun starts being noticeable.

  15. @konstancij

    Shouldn’t it already have reached escape velocity? Id be surprised if there were more burns planned beyond course corrections.
    I assumed the number is not quite accurate, just a ballpark figure?

  16. I am assuming that its the speed relative to Earth as well.

    And I disagree with you slightly on it being meaningless. For the laymen – and considering we are mostly talking about the launch of the spacecraft – it gives a glimpse into the kind of acceleration necessary to escape from Earth; not the exact numbers, but the rough dimension. Yes, you can use that opportunity to teach about relativity. But you can also use it to demonstrate other things, i am not mad at the BBC that they didnt do it at that point (they probably have made numerous documentaries where it came up).

    It is of some value that the layman learns what kind of speeds spacecraft travel around our solar system and what kind of speeds we have to get them to.

    1. @Sebastian,

      In old sci-fi TV shows or movies, characters riding in a space vehicle would occasionally look up from their work and say something like, “The ship has stopped! We are standing still in space!”

      I suppose the navigator had just glanced at the speedometer, and it read zero. Ergo, not moving.

      Seems to me, when discussing a slip as serious as that, it might really be a help to point out that a speed measurement in deep space is “meaningless.” At least that would make more sense than talking about a speedometer.

      At some point, beginners have to realize you can’t just watch space slipping by past your window to figure out how fast you are going.

  17. well, bbc is relatively correct too. May be when one says speed in this context, the speed against earth surface is of main interest, by default and because there is really nothing else. Also there was speed limit of 11.2 for leaving earth orbit, not sure this is the case, but being at 10 kmps it probably will need to accelerate further.

  18. I’ve been wondering about the equivalence of gravitational and inertial accelerations. Take Einstein’s man-in-a-box thought experiment, accelerating at 9.81m/s^2, and another person on Earth. Both will measure an acceleration of the same magnitude, but the direction of the man in the box’s acceleration will be constant, while that of the man on Earth will vary infinitesimally with position (so as to always be towards the center of mass of the Earth.)

    1. Yes; the equivalence is only exact up to the small variations of the sort that you mention. But that level of equivalence is sufficient for many important physical consequences to follow. (In the article above I similarly skirted around the fact that strictly Galilean equivalence only applies if you are traveling in straight steady motion, whereas in fact we rarely do, due to our spinning and orbiting earth; but the important physical consequences of Galilean equivalence often transcend the case of precisely-straight-line travel.)

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