Weighty Spin

By Sean Carroll | April 22, 2008 11:27 am

Remember E = mc2? It’s the one equation that you are allowed to include in your popular-physics book (unless you’re George Gamow, who couldn’t be stopped). Mark gave a nice explanation of why it is true some time back, and I babbled about it some time before that. For a famous equation, it tends to be a bit misunderstood. A profitable way to think about it is to divide both sides by the speed of light squared, giving us m = E/c2, and take this as the definition of what we mean by mass. The mass of some object is just the energy it has in its rest frame — according to special relativity, the energy (not the mass!) will be larger if the object is moving with respect to us, so the mass of an object is essentially the energy intrinsic to its state, rather than that imparted by its motion. Energy is the primary concept, and mass is derived from it. Interestingly, the dark energy that makes up 70% of the energy of the universe doesn’t really have “mass” at all, since it’s not made up of objects (such as particles) that can have a rest frame — it’s a smooth field filling space.

qna_190.jpg All of which is to say that the mainstream media have let us down again. C. Clairborne Ray, writing in the New York Times, attempts to explain whether a spinning gyroscope weighs more than a stationary one, and answers “The weight stays the same; there is no known physical reason for any change.” Actually, there is! The spinning gyroscope has more energy than the non-spinning one. As a test, we can imagine extracting work from the spinning gyroscope — for example, by hooking it up to a generator — in ways that we couldn’t extract work from the stationary gyroscope. And since it has more energy, it has more mass. And the weight is just the acceleration due to gravity times the mass — so, as long as we weigh our spinning and non-spinning gyroscopes in the same gravitational field, the spinning one will indeed weigh more.

Admittedly, it’s a very tiny difference — the energy will increase by an amount proportional to the speed of the spinning gyroscope, divided by the speed of light, that quantity squared, which is really tiny. Nothing you’re going to measure at home. (I’m guessing it’s never even been measured in any laboratory, but I don’t know for sure.) And the article is correct to emphasize that there is no difference in mass that depends on the direction of spin of the gyroscope — that would violate Lorentz invariance, which is something worth looking for in its own right, but would be a Nobel-worthy discovery for anyone who found it.

CATEGORIZED UNDER: Science, Science and the Media
  • Ken

    Given what’s in the body of the response, the intro probably should have stated:

    “The measured weight stays the same; there is no demonstrated method of measuring physical reason for any change.”

  • Ken

    My html sucks and the part “physical reason for” wasn’t stricken through.

    “The measured weight stays the same; there is no demonstrated method of measuring for any change.”

  • M


  • Ellipsis

    A technical question: wouldn’t a more sensitive way of doing such an experiment be to do an update of Pound, Rebka, & Snider using right-circularly vs. left-circularly polarized photons?

    That would seem to me to allow for more precision than weighing an actual gyroscope, no? Is there any theoretical basis for the results differing between spinning photons and a physical spinning gyroscope?

    Any experts around that could answer this?

  • John R Ramsden

    On the subject of the weight of spinning gyroscopes, it might be worth mentioning the late Prof Eric Laithwaite. An amusing account of his long quest can be found at http://www.combat-diaries.co.uk/diary19/diary19chapter_3.htm

  • http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean

    Ellipsis, in general relativity photons of different circular polarizations should propagate along the same paths. The best limit is from cosmology, and the limit on any differential propagation is extremely good.

  • Ellipsis

    Thanks Sean.

  • http://name99.org/blog99 Maynard Handley

    Your intro, however, leaves out, IMHO, the most interesting part.
    What is energy, really?

    One can provide two answers.
    Answer (1) is that energy doesn’t really exist; what exists is that change in fields with time, and energy is another word for how rapidly a (quasi-stationary) quantum field changes with time — ie E=h_bar omega

    Answer (2) is that energy doesn’t really exist; what exists is gravitational curvature, and energy is another word for the 00 term of something (the mass-energy tensor) that ultimately drives spatial curvature.

    Putting these two answers side by side reveals some interesting points.

    (a) The word energy is ambiguous, in that it’s not clear when it’s discussed whether one is referring to (1) or to (2). This is not a completely trivial distinction. The underlying frequency, in the context of (1) can be either positive or negative (the relevant phase of the complex field can rotate clockwise or anti-clockwise), and this matters because it is this choice of rotational direction that gives us particles vs anti-particles. Taking the absolute value of the frequency as energy is a useful convention that is supported by the details of how each interaction works, but is not fundamental. On the other hand, context (2) insists that we are dealing with something positive definite.

    (b) The very fact that this confusion exists is somewhat mysterious and is caused, of course, by the fact that the same engine driving the (very high frequency) temporal modulation of fields is also driving the (low frequency) curvature of space. I’ve never seen a satisfactory argument for why this should be the case, why these things should be linked.

  • http://celsetialmechanician.org Celestial mechanician

    Is the increase in mass gamma for a gyroscope with moment of inertia given by mR^2 where R is the radius of the gyroscope:

    gamma = 1/(1- omega/omega max)^2)^1/2

    where omega max = c/R

  • http://celsetialmechanician.org Celestial mechanician

    Is the increase in mass gamma for a gyroscope with moment of inertia given by mR^2 where R is the radius of the gyroscope:

    gamma = 1/(1- (omega/omega max)^2)^1/2

    where omega max = c/R

  • Ryan

    Regarding: “the energy will increase by an amount proportional to the speed of the spinning gyroscope, times the speed of light, that quantity squared, which is really tiny.”

    Don’t you mean: “…speed of the spinning gyroscope, DIVIDED BY the speed of light…”

    otherwise the increase in energy would be pretty big, right?

  • http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean

    Oops, you’re right; I’ll fix it.

  • andy.s

    Celestial Mech, for small $latex omega$, the extra mass is something like

    $latex frac{Iomega^2}{2c^2}$. Just the rotational energy over $latex c^2$.

    I don’t think you can have an $latex omega_{max}$ for rotation like you have a $latex v_{max}$ for linear velocity.

    Some guy who posts here sometimes wrote a book that touches on this subject.

  • http://tyrannogenius.blogspot.com Neil B.

    I am glad that Sean uses the “old” (relatively old!) definition for mass in relativity! If we define mass according to that “old” STR convention that many of us grew up on [ m = (m_0)(1 – v^2/c^2)^(-1/2) ] then the classic E = mc^2 becomes an accurate formula for the total energy we can derive from a piece of matter, whether at rest relative to us or in motion. The classic formula also tells us the effective inertia of the mass-energy concentration, as noted here. Hence, that convention is better despite the tendency now to refer to “mass” as an invariant (i.e., many now say “mass” for the quantity formerly referred to as “relativistic mass.”) The new definition has the usual snooty appeal to certain kinds of idealism, but: it is hard to keep that definitions straight because of ambiguities in how to define “velocity of the mass” in question, even with relative standards.

    Regarding the example of the gyroscope, that could be in a more extreme case a flywheel inside a container. The rim (with most of the mass) of the flywheel rotates (idealization) at say r*omega = 0.6c. So, its effective mass (for defining either energy, or the weight the whole thing has on the ground, etc.) is increased to the relativistic level of 1.25. But the flywheel is inside a housing and so I don’t see that, so I am tempted to say that the velocity of the “object” is “zero.” That’s one of the problems with the new invariant definition, it is misleading and ambiguous when different parts of “a thing” move at different speeds. With the old gamma factor, you just add up all the relativistic mass. Then the total is consistent, and a proper measure of total energy and total inertia (effective weight for “real gravity” or acceleration by applied force.)

    The inertia of energy, has consequences for the credibility of a universe which has two dimensions of space. The potential for moving say charges together from infinity in such a space is infinite,, so the inertia of their potential energy should be infinite at any separation. This makes physics in 2-d spaces absurd, yet it neither stopped A. K. Dewdney, the author of “The Planiverse, from considering that a plausible physics, nor others writing about things like black holes in 2-space etc. I wonder why?

  • http://tyrannogenius.blogspot.com Neil B.

    Andy S., pls. tell me how to imbed symbols/equations in my comments?

    PS: Interesting to note, as far as “measured” goes, that no one has yet directly measured Lorentz contraction, true? Isn’t that ironic, with all the complaints about the failures of pseudoscience and etc? Sure, LC makes logical sense (just consider the need to be consistent with time dilation when one body passes another – the alternative is unequal approach velocities!), but to never have been actually measured … If this was something really controversial, we’d hear flack about it!

  • big vlad

    I much prefer the modern convention in which mass is an invariant. So I would say E = gamma mc^2. In this convention the mass of the gyroscope would stay the same, but its energy would increase due to the gamma factor.

  • http://vacua.blogspot.com Jim Harrison

    Don’t you have to make a relativistic correction to various thermodynamic equations to take into account the greater mass imparted to a (very) hot gas by the motion of its component molecules?

  • Nicholas

    This reminds me of a story I heard of someone who apparently asked Apple customer service if his iPod would get heavier as he put more songs into it. The question is laughable at first, because songs are just information — surely information doesn’t weigh anything!

    But that got me wondering: would the iPod, in fact, get heavier? It seems conceivable to me that its weight might change, since (according to my extremely skimpy understanding of hardware) the information in the iPod is stored in the form of spin states, and these spins might get flipped as a result of adding songs, possibly changing the net energy of the iPod (e.g., from classical electromagnetism the energy of a magnetic dipole is lower if the dipole is parallel to the magnetic field than if it’s anti-parallel.) But I don’t really know in detail how iPods work. Could someone illuminate this to me?

    It would be funny if iPods do actually get heavier when you add songs to them. It’d be even funnier if whether or not the weight changes depends on the kinds of songs you add, so for example, Beethoven might cause your iPod to get heavier whereas the Beatles might cause it to get lighter. The Beatles would then have a negative “iPod mass”! Perhaps the possible negativity of the iPod mass could shed light on the nature of inflation and similar problems in physics… in fact, I’m sure Apple is already working on such a product: the i-Cosmology.

  • http://countiblis.blogspot.com Count Iblis
  • http://deleted Simon DeDeo

    Nicholas — my guess: maybe. If you think of the hard drive as a bunch of little bar magnets. As long as they cooled the material it was made of slowly enough, it will be in a rather low energy state — the bar magnets will all be anti-aligned.

    As you add songs, of course, you start flipping that bar magnets around — most likely out of their minimum energy state. So the energy of the system goes up, and when you divide your iPod by c^2, yes, it is more massive. My guess is that music has a rather high — near maximal — entropy, especially after being compressed as an mp3.

    This doesn’t hold if the hard drive is “zeroed out”, or if the drive material was cooled too fast (not properly annealed.) In the latter case, the bar magnets had very little correlation to begin with (i.e., high entropy) because they were frozen in at a very high temperature.

  • http://tyrannogenius.blogspot.com Neil B.

    Correction – I should have said
    ” … (i.e., many now say “mass” for the quantity formerly referred to as “proper mass.”) ”
    I think the iPod thing about increased mass is cute. How about human brains?

  • http://deleted Simon DeDeo

    Also: gyroscopes spinning and having weight. What’s the amplitude of the general relativistic spin-spin coupling of the gyro-Earth system? It should also come in at order c^2, but instead of two factors of the gyro velocity, it’s one gyro, one Earth.

  • http://tyrannogenius.blogspot.com Neil B.

    Iblis, I clicked on a real physics link (http://www.claymath.org/millennium/Yang-Mills_Theory/ ) from that joke computer warnings page, and got this interesting scoop that I didn’t know about:

    The successful use of Yang-Mills theory to describe the strong interactions of elementary particles depends on a subtle quantum mechanical property called the “mass gap:” the quantum particles have positive masses, even though the classical waves travel at the speed of light. This property has been discovered by physicists from experiment and confirmed by computer simulations, but it still has not been understood from a theoretical point of view. Progress in establishing the existence of the Yang-Mills theory and a mass gap and will require the introduction of fundamental new ideas both in physics and in mathematics.

    What’s up with all that, and why don’t we hear more about it? tx

  • http://deleted Simon DeDeo


    Hmm. I mean, totally different set-up, and totally different domain of validity, but it does indeed go as



    GMM’v_E v_G / r_E r_G c^2

    which is, on the face of it, quite a bit larger than

    GMM’ v_G^2 / r_E^2 c^2

    given the smallness of r_G compared to r_E, and v_E is about 100 m/s (a possible gyro speed.)

    Sean, you wrote the book on this. Is it possible that the relativistic spin-spin coupling could dominate over the gravitation of the kinetic energy?

  • aatish

    bigvlad, I was wondering the same thing. But even in the modern convention, where mass is invariant so we have E = gamma m c^2, doesn’t gamma depend only on the translational velocity of the centre of mass? In the case of the gyroscope if you are in it’s rest frame (i.e. where it’s spinning but not translating), so gamma is 1 but as Andy S. pointed out, the $latex frac{Iomega^2}{2c^2}$ term should still contribute to the mass.

    I’m not sure I understand this, though. Does it work like this: gamma m c^2 includes the translational kinetic energy, so the E must include all other forms of energy (potential and rotational kinetic energy)?

  • http://deleted Simon DeDeo

    ack — clearly the spin-spin coupling can’t be independent of distance between the gyros. Looks like there has to be a dimensionless factor of something like (r_G/r_E) (comparing with the dimensionless factor in the paper linked above — spin-spin force declines as 1/r).

    But that would still leave the spin-spin coupling relevant at the level of the gravity of the kinetic energy.

  • http://blogs.discovermagazine.com/cosmicvariance/sean/ Sean

    I’m certainly using the “modern” terminology, in which mass is invariant. (By which we mean “invariant under Lorentz transformations.”) That’s why I wrote “the energy (not the mass!) will be larger if the object is moving” above.

    Simon, I don’t know about the spin-spin coupling. GR and SR effects are numerically comparable for GPS satellites, so maybe.

  • http://tyrannogenius.blogspot.com Neil B.

    But Sean, if we use the “old” usage of relativistic mass to refer to plain “m” when not zero-subscripted (and I do follow the recent history of science terminology to some extent, that is what most writers used to say) then we can use “mass” in a way that actually makes this sentence of yours consistent:
    A profitable way to think about it is to divide both sides by the speed of light squared, giving us m = E/c2, and take this as the definition of what we mean by mass.
    That doesn’t really square, pardon the pun, with what you said after that. The relation m = E/c2 is only true in general if we *do* include the energy of motion etc. That is the whole point of my own illustration about the extra “mass” in the gyroscope, the “rest frame” of the gyroscope as a whole does not follow the motion of the rotor – hence, the “mass” of the gyroscope as a whole is higher despite the *sums* of the “rest masses” being the same. That is just confusing, but summing “relativistic masses” always gives the same number in a given reference frame.

    But OK, for convention we can just call the augmented quantity “relativistic mass,” and you can reserve “mass” for the “rest mass” if you want. However, considering the internal motions and mass deficits etc. involved in talking about matter, I consider the latter concept to be awkward. Also, we might as well keep the zero subscript just to be sure what is being referred to.

  • http://web.mit.edu/sahughes/www/ Scott H.

    Simon, it’s pretty easy to show that the spin-spin energy will be quite small compared to the kinetic energy associated with the rotation. Forgive the lack of latex in this little comment, this may end up looking ugly.

    Working in units where G = c = 1, the spin-spin energy is (up to factors of order unit, and neglecting angular factors)

    E_ss = (Searth)(Sgyro)/r^3

    where Searth and Sgyro are the spin angular momenta associated with the earth and with the gyro. The correct value of r to use here is the radius of the earth; this formula comes from considering the torque that acts on a gyroscope due to the “gravitomagnetic” frame dragging field of a spinning body. Note the resemblance to a magnetic dipole sitting in a magnetic field; note also that this interaction energy falls off quite rapidly with distance. (Since in G = c = 1 units angular momentum is a length squared, this formula is dimensionally consistent.) It’s this one over r cubed that is going to kill this. The kinetic energy associated with the gyro can be written

    E_gyro = (Sgyro)^2/(2 Igyro)

    where Igyro is the moment of inertia of the gyroscope. The ratio of these two formulas is

    (E_gyro)/(E_ss) = (Sgyro) (Rearth)^3/(Igyro Searth)

    (dropping the annoying factor of two at the level of precision with which we’re making this estimate). Searth = Iearth Omegaearth, and the moment of inertia of the earth is Iearth = (factor that depends on the concentration of the earth’s mass ~ 0.3 or so) times Mearth Rearth^2. Also, Sgyro/Igyro = Omegagyro.

    Putting all this together, we have

    (E_gyro)/(E_ss) = (Omegagyro Rearth)/(Omegaearth Mearth).

    Since we can easily make the gyro spin faster than once per day, and since Rearth/Mearth ~ 10^9 (in G = c = 1 units), the spin-spin interaction is pretty small compared to the kinetic contribution.

  • http://deleted Simon DeDeo

    Hey Scott — something odd here for me in your derivation? It’s not the energy associated with the spin-spin coupling, but the force itself. i.e., your calculation seems to assume that the spin-spin force is caused by the gravitation of the energy associated with it. Which seems strange? (For example, the potential energy of the gyroscope does not lead to much of an additional gravitational force — it’s the gradient of the potential field itself that dominates!)

    Here’s what I would say (I agree with you on the magnetism analogy, BTW — I am not sure why the paper I linked found a 1/r dependence for the force, I agree it should be 1/r^4.)

    F_ss = (Searth)(Sgyro)/r^4

    F_gyro = Mearth(Sgyro)^2/(2 Igyro)/r^2


    F_ss / F_gyro = omegaearth / omegagyro

    OK, so I agree — highly subdominant. Also, it is very stressful to do simple algebra in front of millions of people.

  • Mike M

    PS: Interesting to note, as far as “measured” goes, that no one has yet directly measured Lorentz contraction, true?

    Doesn’t that depend what you are prepared to accept as a measurement? For example, interferometric techniques provide the most accurate length determinations there are, so it might reasonably be argued that the Michelson-Morley experiment was a very direct measurement of Lorentz contraction.

    Personally, I still can’t get over the notion that if you measure a magnetic field due to current in a wire, you are actually measuring the electric field arising from the differential in Lorentz contraction between the positive and negative charges in the wire, due to the mm/s drift velocity of charge. So, anyone who has ever done high school physics has measured Lorentz contraction arising from snail’s pace velocities.

  • John R Ramsden

    Scott (#29) and Simon (#30), or anyone come to that, in the context of GR if two rotating rigid bodies are in mutual orbit in space, unaffected by other masses, and their rotation axes ae skewed, will GR effects tend to evolve their rotation axes over time to be anti-parallel?

    I realise this would be a miniscule effect, if it existed at all, and probably dwarfed even by the small tendency to spiral towards each other as energy dissipated from the system by gravity waves. But I’d be very interested in a sketch of the kind of calculations that might be involved or a reference.

    (Also, let’s assume the bodies’ rotation rates are each synchronized with their orbital speeds, or that they are black holes say, so that energy is not lost from the system by thermal radiation caused by distortions changing the bodies’ shapes as they rotate.)


    P.S. On the off-chance you might have a comment, but prefer not to wrestle
    with TeX notation here or risk remarks open to challenge, my email is jhnrmsdn at yahoo dot co dot uk, although obviously a reply would ideally be better here for everyone’s benefit.

    Also, if I receive any relevant emails on this (small chance, but one lives in hope!) I’ll summarize them anonymously here, unless the sender explicitly consents to their name being cited.

  • chris

    hi nicholas (#18),

    i actually would expect the ipod to get lighter when you store songs. since the process of storing songs involves energy, a fraction of which will be dissipated and radiated off, the net mass will be lower afterwards.

    that is if you ignore such huge effects like the fingerprints on the button when you initiate the recording or the associated material loss (paint e.g.), that i would estimate to be at least 10 orders of magnitude more important.

  • chris

    niel B (#23),

    that is one of the millenium challenges. i don’t know in what respect you can expect to hear more about it, since it is a purely formal mathematical problem.

  • http://web.mit.edu/sahughes/www/ Scott H.

    Hi Simon —

    I think we were just calculating slightly different things. I wasn’t thinking forces, just energies. For the weight of a gyroscope, I agree it’s the force you want, and is certainly the relevant quantity. Sorry to get off topic … chalk it up to blog scanning just before going to bed.

    Note that the spin-spin energy I was looking at does indeed lead to the 1/r^4 force you calculated; however it also causes a 1/r^3 torque which causes gyroscopes to precess (torque ~ dE_ss/dAngle). One can interpret the GP-B frame dragging precession as due to this torque — the gyro tries to realign to minimize the interaction energy.

    John Ramsden, these couplings lead to precession, but do so in such a way that the *total* angular momentum remains conserved. In other words, you can define J_total = L_orbit + S_1 + S_2, and you find that spin-spin (and spin-orbit) tend to change the direction, but not the magnitude, of S_1 and S_2. In order that J_total be constant, L_orbit “recoils” to compensate. One never finds that the orbits become antiparallel; the components of S_i parallel to J_total remain fixed, while the components perpendicular to J_total precess around. Note that some evidence for these precessions has been seen in binary pulsar systems.

    Whoever said Lorentz contraction hasn’t been observed … well, time dilation is observed all the time. Certain cosmic rays (e.g., muons) that are produced in the upper atmosphere should decay before reaching the ground. But, they easily make it thanks to their dilated lifetime. Even more extreme dilation is observed in particle accelerators every day — fast moving particles cover a distance that is set by their dilated lifetime. In the frame of the particle, the lifetime is just the rest lifetime, but the distance is length contracted, so everything is consistent. (Even more prosaically, the existence of magnetic forces from electric charges is a simple consequence of length contraction — see chapter 5 of the E&M textbook by Purcell.)

  • Eastsider

    In response to Mike M — is it not correct that Lorentz suggested the contraction to EXPLAIN the result in the Michelson-Morley experiment? Thus by definition the Lorentz contraction was demonstrated by that experiment.

  • anon

    would a rotating galaxy’s increase in mass affect
    dark matter calacultations?

  • http://web.mit.edu/sahughes/www/ Scott H.

    would a rotating galaxy’s increase in mass affect dark matter calacultations?

    No … the rotation affects things by a fraction (vrot/c)^2, which is like a part per million or so. To explain galaxy rotation curves you need a factor of several change in the mass estimate. (It’s also worth noting that rotation curves are just one of many lines of evidence suggesting the need for dark matter. Even if one could cook up a model that explained galaxy rotation, you’d still need to explain galaxy cluster dynamics, x-ray temperatures of bound gas in clusters, gravitational lensing, and the amplitude of acoustic peaks in the cosmic microwave background … and probably a few other things that I’m forgetting.)

  • Xerxes

    Whoever said Lorentz contraction hasn’t been observed … well, time dilation is observed all the time.

    For a real-life example of Lorentz spatial contraction rather than time dilation, consider the RHIC experiment. Their models depend on the shape of the interaction region where two nuclei collide, so it’s important to remember that the normally spherical nuclei will be flattened into pancake shapes at relativistic speeds.

  • Xenophage

    Spinning Earth, tidally-locked moon, both in free fall around the sun. No spin Nordtvedt effect. No free fall spin effects in Gravity Probe B’s two sets of opposite spin-paired gyroballs. No orbital weirdness for mismatched binary pulsar PSR J0737-3039A/B (arxiv.org/abs/astro-ph/0609417). No vacuum dispersion, dichroism, or gyrotropy for linearlyly polarized light (50:50 mix of left and right circular polarizations) over millions of lightyears path through vacuum.

    Is the vacuum isotropic? To EM, yes! (arXiv.org/abs/0706.2031). To physical spin, gravitational binding energy, composition, quantum particle and orbital angular momenta (http://www.npl.washington.edu/eotwash/publications/pdf/prl97-021603.pdf), magnetism, superconductivity… yes! To better than parts-per-trillion relative.

    However… given chemically identical opposite parity mass distributions a first order Equivalence Principle violation arises from their diastereotopic interaction with a massed sector chiral vacuum background (opposite shoes fitted onto a left foot) in teleparallel gravitation with Weitzenböck spacetime torsion (transforms like Lorentz force in EM).

    Perform a parity Eötvös experiment opposing enantiomorphic space groups P3(1)21 and P3(2)21 solid single crystal quartz test masses (opposite parity spatial distribution of atoms). Cultured quartz is a commercial product with exacting specifications. It is the only place nobody has looked. It is supported by orthodox classical gravitation theory that wholly includes GR as as restricted case. That case may be demonstrated incomplete without contradiction of prior observations.

  • andy.s

    Neil B. check out this thread for bloggy equation goodness:

    Succumbing to Latex

  • http://tyrannogenius.blogspot.com Neil B.

    Mike M, Scott H., Eastsider: I am well aware of the examples you give, that is why I carefully said “direct” measurement of Lorentz contraction. I meant direct in the strict conventional sense, of finding the length shorter by actual point to point comparison and not by any kind of inference, however convincing (and some are, but that isn’t the point when you refer to the strict definition of “direct”. I already said that LC is needed for consistency with time dilation, but that isn’t “direct,” nor is the inference that it only makes sense to imagine magnetic forces if we image LC of the line of charges, etc, sure. As for the MM experiment, LC is a theory to explain the null results: good and perhaps necessary, yes, but not “direct” in logical terms. It does not “prove” the LC, because there would also be a null MM result if for example “ballistic” (Galilean-style velocity addition) applied to light. Folks – you need to tighten up on the strictness of your semantics!

  • http://tyrannogenius.blogspot.com Neil B.

    andy S: tx for the LaTeX info.

  • Richard E.

    The magnetic field of current carrying conductor can (and should) be understood as a purely relativistic effect — you can derive it from electrostatics and the Lorentz transformations. You “observe” a length contraction every time you use an electric motor, and the (average) velocities involved are all tiny :-)

  • http://deleted Simon DeDeo

    Neil, you do have a rather strict notion of direct! I don’t think we’re going to have Lorentz contraction qualia anytime soon, and there’s no “logical” notion of directness for inductive reasoning. E&M is good enough for me, indeed it’s hard to see how you could make a “point to point” measurement of Lorentz contraction because it would come down to the famous “pole-barn” thought experiment which famously turns into a question of simultaneity — but you’ve rejected time dilation as sufficient to establish length contraction.

    In general, you need a set of background assumptions to do any kind of science; you can’t establish Lorentz contraction without holding, and inferring from, some other beliefs about the nature of the physical world. Logically speaking, every measurement we’ve made is compatible with the absence of Lorentz contraction, but the amount of background you’d have to alter at this point is huge.

  • http://tyrannogenius.blogspot.com Neil B.

    Simon, et al, the acceptance of simultaneity is indeed required in order to define “length”, but then once so accepted, the “length” has to be “directly” measured by finding endpoints at simultaneous times. (Well, I accept one other definition that is presumably equivalent: once we accept a “velocity” of a body, we can use how long it takes to pass a given point – but even then we need to define “velocity”. Actually that doesn’t require simultaneity if we can segue to rotary motion: you could use a large wheel of known circumference and take the period! This has interesting implications not often discussed anymore. Remember the old “Ehrenfest paradox”, and the related issues of elastic strain in a LCed rotating rim?)

    That is what “direct” means, it is not too strict; you folks are too post-modernistically mushy etc. IMHO. If you use background assumptions and reasoning to infer something, well, it is still “inferred”, good practice or not. I’m not saying it’s wrong to believe in what is well inferred (I believe in LC too for all the same reasons), but I care about good use of wording – shouldn’t you?

    BTW, what do any of you think of the proposition I put upthread, that we should use “mass” in the sense of “relativistic mass”? See my arguments for why it is better than the invariant “proper mass” as a placeholder for “mass” in general.

  • http://deleted Simon DeDeo

    But Neil, whatever “point to point” measurement you make will require some background assumptions — if only in the physics of your measurement system! There’s really no way you can get a “direct” measurement.

    If you are not willing to take the equivalence of frames as a given (from which time dilation gives you length contraction), then you are so crazy as to let anything go. You could measure length contraction but then say, oh, motion creates a mystical field that affects my measurement devices in a systematic way.

    You suggest using a spinning disk to get around questions of simultaneity. The resolution of that paradox is far more “background loaded” than barn-pole, but let’s ignore that. I’ll do the experiment, but instead of painting dots on the sphere and watching them go by (your example of a “direct” experiment, I think), I’m going to charge it up and measure the magnetic field. There’s really no way you can separate those two into distinct epistemological categories (unless you have some wacky notion of qualia as ontologically prior — but I doubt you’re a Heideggerian!).

    They are on a continuum and no “good use of wording” will make the difference discrete. Indeed, dots-on-a-sphere may require a great deal more background assumptions — about the nature of light propagation, for example — and the visual experience will have to be disentangled because of doppler shifts and so forth! I’m not particularly “post-modern” (whatever that means), but neither am I a logical positivist. This is pretty standard Quine stuff.

    As for terminology questions of which mass is the “true” mass. In teaching relativity I find it’s nice to make a distinction between “number of atoms” (proportional to rest mass) and “mass”, the latter of which I define through inertia. Relativity does force us to complexify our intuitive ideas about “mass as stuff”, though, so perhaps we should bite the bullet and call them “zoog” and “zaag”.

  • Mike M

    That is what “direct” means, it is not too strict; you folks are too post-modernistically mushy etc. IMHO. If you use background assumptions and reasoning to infer something, well, it is still “inferred”, good practice or not. I’m not saying it’s wrong to believe in what is well inferred (I believe in LC too for all the same reasons), but I care about good use of wording – shouldn’t you?

    Perhaps we should. Perhaps we don’t like being patronized. Or perhaps we are smart enough to recognize that it isn’t that simple. Why is using a ruler the “direct way” to measure a length? Isn’t counting the clicks on a click wheel a direct way to measure a length? Or perhaps sonar, which you have already accepted as a direct measurement, since it involves measuring the time it takes something (in this case a sound wave) to travel at fixed velocity from one end to the other. Why not time a light wave? Or you could lay a bunch of cigarettes of known length end to end and count them, which, I hope you agree, is really just a rather foolish kind of ruler. In fact, you could use any standard rod you like for the measurement: pingpong ball, cricket stumps, you name it. They are all rulers. Or even wavelengths of light of known frequency: you could set up a standing light wave and count the nodes. That would be an interferometer, which, I am sure you now agree, is just a ruler. So perhaps Messrs Michelson and Morley were just using a ruler to make a direct measurement, and we weren’t the ones who hadn’t thought through what constitutes “good use of wording.”

  • http://tyrannogenius.blogspot.com Neil B.

    Well gee whiz, I stirred up quite a bit of wrangle hear which I suppose is what science and the philosophy of is all about. What I meant was, no one has yet measured a moving meter (at rest) stick by comparing endpoints, to say “Hey, we got 0.9999995 meters of length and it’s going 0.01 c, so we confirmed Lorentz contraction by direct measurement.” All that discussion about the sort of things that should also count is OK, but that just hasn’t been done whatever you want to call it, or call the related ways to find out. Can we agree at least on that?

  • http://tyrannogenius.blogspot.com Neil B.

    Oops make that 0.001 c.

  • Mike M

    I agree that no-one has ever done that experiment, because measuring such tiny differences is impractical using something as crude as a meter rule . Equally, no-one has ever demonstrated that the Moon is not made of cheese by seeing what Moon rock tastes like. After all, that’s certainly the direct way of doing it, and using mass spectrometers, chromatographs, etc, well that just leads to an indirect inference that the Moon doesn’t have at least a slightly cheesy flavor. Fortunately, it is in the nature of science that we accept such inference when the “direct” way of doing something is impractical.

  • http://samthornton.blogspot.com Sam Thornton

    In exploring some links related to this article, I was brought by the commodious vicus of internet recirculation to a series of articles on fusion energy technology. Turns out the science and the basic engineering were solved in October 2006 by a Navy R&D project led by now deceased scientist, Dr. Robert Bussard, former Asst. Director of the Atomic Energy Commission.

    Although October 2006 marked the breakthrough, it also marked cancellation of the project by the Bush Administration, which needed the insignificant amount of further engineering development money for the Iraq War.

    Here’s a link to a video of a talk about the project Dr. Bussard delivered to Google employees before he died.

    Here’s a link to an interview he gave about the technology.

    How about it, Cosmic Variance? An article on this would be great.

  • http://tyrannogenius.blogspot.com Neil B.

    Mike, the kind of physical-chemical analysis done of Moon rocks is of course “direct” – it doesn’t require human taste buds, good grief. I’ve made my case to the extent that any fair observer would concede the issue. I think we have a case here of people just wanting to keep on pounding their original line out of misguided stubbornness, vanity, or whatever even after a good argument has been made against their perspective. This is as unhealthy as it is dismayingly commonplace.

    “What we’ve got here is a failure to communicate!” – the Boss from Cool Hand Luke

  • http://tyrannogenius.blogspot.com Neil B.

    PS – Of course you also forgot the theoretical basis for LC being good, but me just saying “We haven’t’ measured it directly” (and I keep saying, I don’t give a damn that we haven’t, I believe in it too but just want that admitted), versus the poor theoretical basis for saying the Moon is made of green cheese. So now are you going to argue with that too, just so you don’t have to ever concede to anyone?

  • Mike M

    I think we have a case here of people just wanting to keep on pounding their original line out of misguided stubbornness, vanity, or whatever even after a good argument has been made against their perspective. This is as unhealthy as it is dismayingly commonplace.

    I congratulate you on a rare moment of insightful introspection.

  • http://tyrannogenius.blogspot.com Neil B.

    Heh – I said good argument, that’s what I was waiting to hear from anyone else. I’m not sure you’d know if it was rare for me to get that general point, whether intro- or extro- spection is the best spin on it.

  • andy

    hey Mike, maybe you should go and check for yourself if the moon is made of cheese. that would dissuade you of many things to believe in.

  • Mike M

    It’s a shame that neither you nor Neil actually read what I wrote. If you had, you would see that I likened the requirement that one “directly” measure Lorentz contraction (a thing most people believe to be true) using a meter rule (a completely impractical way to make such a measurement) to testing the hypothesis that the Moon is not made of cheese (a thing most people believe to be true) “directly” by tasting it (a completely impractical way to make such a measurement).

    Personally, I am happy to accept the measurements of spectrometers, etc, as the more appropriate way to measure the composition of the Moon and hence show directly that it doesn’t taste of cheese, just as I am prepared to accept interferometric measurements of distance as the appropriate way to measure directly the very small effects of Lorentz contraction in the laboratory.

    The fact that no-one has used a meter rule to do so may well be true, but it is entirely uninteresting as using a meter rule to measure such a distance is no more “direct” a measurement than using interferometry, just as the fact that no-one has actually tasted Moon rock may well be true, but is uninteresting because tasting Moon rock is no more “direct” a measure of its cheesiness than using a mass spectrometer.

    Was that spelled out explicitly enough this time?

  • http://tyrannogenius.blogspot.com Neil B.

    Well Mike et al, maybe we can gracefully wrap this one as follows: First, again, I was referring simply to whether Lorentz contraction had been “directly” measured in the strictest way as a matter of historical interest, not whether it needed to be to warrant our belief, whether practical or not, etc. Claims per se shouldn’t be harried over extraneous matters; such matters should be made as side points. As for whether interferometer measurements should count as “direct”: Sure, once we are assured of the Einstein postulate about light speed constancy. But as I said, the null result of the MM experiment could of course in principle have derived from Galilean behavior of light propagation. So, accepting interferometer results depends on “auxiliary assumptions”, warranted as they may be. It could be a matter of semantics in philosophy of science whether that can be called “direct,” maybe we can just say it’s a judgment call depending on how anal retentive one is.

    In any case, here’s a quote from one of the top physicists in the field. He supports my position exactly and the situation hasn’t changed since then:

    “It is an amazing fact that there does not seem to exist any direct or simple experimental verification of the Lorentz-Fitzgerald contraction. There is no reason whatever to doubt that the effect exists, precisely as called for by theory. So far, nevertheless, the difficulties – (1) of securing an object of appreciable length that moves with a speed comparable to that of light and, (2) of determining two events, one at either end, which are simultaneous for the observer – have proved insuperable. This very fundamental conclusion of the theory awaits actual proof.”

    Albert Shadowitz, Special Relativity, 1968, p. 168 of Dover paperback.

  • Mike M

    The only problem with asking a famous physicist is that he is unlikely to have ever traveled anywhere sufficiently relativistically to be in with a shot of whipping his ruler out to measure Lorentz contraction. Surely, more productive to seek the views of a cosmic ray muon, whom you would never have met at all if he hadn’t just “directly” measured the Lorentz contraction of the Earth’s atmosphere as it flew past him.


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Cosmic Variance

Random samplings from a universe of ideas.

About Sean Carroll

Sean Carroll is a Senior Research Associate in the Department of Physics at the California Institute of Technology. His research interests include theoretical aspects of cosmology, field theory, and gravitation. His most recent book is The Particle at the End of the Universe, about the Large Hadron Collider and the search for the Higgs boson. Here are some of his favorite blog posts, home page, and email: carroll [at] cosmicvariance.com .


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