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If the Michelson-Morley experiment hadn't been conducted, are there any other reasons to think, from the experimental evidence available at that time, that Einstein could think of the Special Theory of Relativity?

Is there any other way to think why the speed of light is the ultimate speed limit?

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    $\begingroup$ back in the days of M&M? or today? $\endgroup$ – AccidentalFourierTransform Dec 15 '16 at 13:39
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    $\begingroup$ Back in M&M days.. actually before Einstein's STR and Now too... Do we still know anything other than M&M?.. $\endgroup$ – Vivekanand Mohapatra Dec 15 '16 at 15:47
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    $\begingroup$ Well, perhaps because when you put particles in an accelerator and accelerate the heck out of them, they refuse to go faster than light. Experiment trumps theory :-) $\endgroup$ – jamesqf Dec 15 '16 at 18:40
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    $\begingroup$ Perhaps the question would be clearer if it said "was there" rather than "is there", since it's asking about what was available to Einstein. $\endgroup$ – Glen_b Dec 15 '16 at 21:37
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    $\begingroup$ I asked a similar question to this on HSM SE a while back, which may be worth a read: hsm.stackexchange.com/questions/2088/… (particularly Ben Crowell's comment) $\endgroup$ – Quantum spaghettification Dec 16 '16 at 18:43

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A lot of people find it somewhat surprising, but Einstein's initial formulation of special relativity was in a paper, On the electrodynamics of moving bodies, that makes very little reference to the Michelson-Morley result; instead, it is largely based on the symmetry of electromagnetic analyses in different frames of reference.

From a more modern perspective, there is a strong theoretical case to be made that special relativity is, at the very least, a strong contender for the description of reality. These are beautifully summed up in Nothing but Relativity (doi), but the argument is that under some rather weak assumptions, which are essentially

  • the homogeneity and isotropy of space, and
  • the homogeneity of time, plus
  • some weak linearity assumptions

you are essentially reduced to either

  • galilean relativity, or
  • special relativity with some (as yet undetermined) universal speed limit $c$,

with no other options.

To get to reality, you need to supplement this theoretical framework with experiment - there's no other way around it. The Michelson-Morley experiment is, of course, the simplest piece of evidence to put in that slot, but in the intervening century we have made plenty of other experiments that fit the bill. From a purely mechanical perspective, the LHC routinely produces $7\:\mathrm{TeV}$ protons, which would speed at about $120c$ in Newtonian mechanics: it is very clear that $c$ is a universal speed limit, because we try to accelerate things faster and faster, but (regardless of how much kinetic energy they hold) they never go past $c$.

If you want something from further back, this is precisely the reason we developed the isochronous cyclotron in the late 1930s and then switched to synchrotrons back in the 1950s - cyclotrons require particles to keep in sync with the driving voltage, but if they approach the speed of light they can no longer go fast enough to keep up. We have upwards of eighty years of history of being able to mechanically push things to relativistic regimes.

If you wish for an answer inscribed within "experimental physics as of 1888, minus the Michelson-Morley result" then, as I said, the symmetry properties of electromagnetism (which are directly compatible with SR as derived from $v\ll c$ experiments, but require aether theories to make sense in galilean relativity) were plenty to convince Einstein that SR was the right choice.


Edit:

As pointed out in a comment, Einstein's original paper does make some reference to Michelson-Morley(-type) experiments, in his second paragraph:

Examples [like the reciprocal electrodynamic action of a magnet and a conductor], together with the unsuccessful attempts to discover any motion of the earth relatively to the “light medium,” suggest that the phenomena of electrodynamics as well as of mechanics possess no properties corresponding to the idea of absolute rest.

However, apart from this small nod, he makes no substantive references to the aether or its equivalents: the paper starts with the relativity postulates (based on the constancy of the speed of light), uses those to construct special relativity (as pertains transformations between moving frames, and so on), and then builds his case for it on the transformation properties of the equations of electromagnetism: these provide the deeper fundamental insight that underlies the symmetry of analysis of electromagnetic situations performed on different moving frames of reference.

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    $\begingroup$ While it is true that Einsteis's paper does not include a reference to M&M, he does refer to the "unsuccessful attempts to measure the speed of Earth relative to the ether" or words to that effect. He must surely have been referring to M&M if only indirectly. I'm a member of a reading club that recently read that paper and was surprised to see that quote in light of the common lore that he did not use M&M. $\endgroup$ – Lewis Miller Dec 15 '16 at 16:14
  • $\begingroup$ @LewisMiller Thanks for that - I should re-read that paper a bit more closely, it's been some time. The rest of the answer still stands, though - and indeed, as far as Einstein goes, referring to a lack of a positive result rather than a specific negative result is rather different. $\endgroup$ – Emilio Pisanty Dec 15 '16 at 16:16
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    $\begingroup$ To be more specific, Einstein noticed that the equations governing EM waves yielded a speed that made no reference to the medium supporting the waves. $\endgroup$ – LastStar007 Dec 15 '16 at 22:37
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    $\begingroup$ @LewisMiller There were other "unsuccessful attempts" to measure the speed of light during Einstein's time, namely the experiments on the stellar abberation of light, and Fizeau's measurements on the speed of light in water. It's not a common lore that he didn't consider M&M, but it came from Einstein himself. $\endgroup$ – Maxis Jaisi Dec 16 '16 at 7:44
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    $\begingroup$ @MaxisJaisi It did come from Einstein in his later recollections regarding SR, but there are earlier statements disputing this claim (also from Einstein). I found this link: link.springer.com/article/10.1007/s00407-009-0050-5 that may be of interest. It gives a balanced treatment of this question and includes newly available resources that shed some light on the issue. $\endgroup$ – Lewis Miller Dec 16 '16 at 20:57
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In the modern day we have very direct measurements of the velocity behavior of particles as you add kinetic energy. The CEBAF accelerator at Jefferson Lab only works because adding (a lot!) more energy to the electrons after they have entered the racetrack for the first time doesn't change their speed relative the lab enough to be measured.

Really.

Between leaving the booster with 123 MeV kinetic energy and being delivered to the halls with up to 12 GeV kinetic energy (a factor of ~100 increase) the beam speed stays constant to high precision.

In calculations this means we go from $\gamma_\text{booster} = 241$ to $\gamma_\text{max} = 23500$. You'll need a high precision calculator to determine the difference in speeds implied by this and the real world bears such considerations out.

You just can't push a particle faster than $c$.

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    $\begingroup$ Honest question: if it's not going faster, how do you (experimentally, in the lab) know that it actually does have a higher kinetic energy? $\endgroup$ – Emilio Pisanty Dec 15 '16 at 18:59
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    $\begingroup$ @EmilioPisanty Its momentum grows. The beam has to be separated into components before each of the curved section so that each subbeam can be sent through a separate beamline with the right magnet tune for that subbeam's momentum to make it around the bends. And of course, the subbeams have to be recombined before re-entering the acceleration runs along the straight sides. CEBAF is a ridiculously ambitious machine that works better than anyone could have hoped. It's a testament to the designers and operators. $\endgroup$ – dmckee Dec 15 '16 at 19:03
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    $\begingroup$ So you have an easy measure of how much force you need to accelerate the particle sideways? Yeah, that's pretty clever. It's still not quite a direct measurement of energy, though. (I ask because I washed over it in my answer, but the perspective from someone in the trenches is way better.) $\endgroup$ – Emilio Pisanty Dec 15 '16 at 19:06
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    $\begingroup$ The energy added is a function of the field strength in the cavities and because of the significant beam intensities can actually be measured (in a collective way) by the power needs of the cavities (relative no-beam). Moreover theory tells us that the energy added to each bunch depends on the frequency, the speed of the bunch and the phase shift relative the nominal synchronization (with lagging particle getting a little more than leading particles leading to improved bunch coherence). Beyond that I'm out of my depth and you'd have to ask an accelerator physicist. $\endgroup$ – dmckee Dec 15 '16 at 19:13
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    $\begingroup$ I suppose an argument that this is a more direct measurement of speed as a function of momentum, but it leads to the same conclusion that you just can't push the beam faster than $c$. $\endgroup$ – dmckee Dec 15 '16 at 19:14
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The Fizeau experiment is a way to measure the speed of light in a moving medium. From our modern standpoint, it provides an experimental test for the Lorentz transformation of a velocity $u$ in a reference frame moving at $v$, in the regime where $u$ is of order $c$ and $v \ll c$. Crucially, the apparatus is sensitive enough to discriminate the Lorentz transformation formula $u' = \frac{u + v}{1 + \frac{uv}{c^2}}$ from the Galilean formula $u' = u + v$. The experiment was conducted in 1851, which was 36 years before the Michelson-Morley experiment.

Fizeau's results were unexpected at the time, disagreeing with naive ether-drag theories. However, the response among theorists was to favour more convoluted ether-drag theories, where different materials dragged the ether to different extents. These theories grew even more complex to incorporate dispersion, i.e. different wavelengths of light having different refractive indices.

Here are the conclusions drawn by Fizeau (emphasis mine):

Either, first, the æther adheres or is fixed to the molecules of the body, and consequently shares all the motions of the body; or secondly, the æther is free and independent, and consequently is not carried with the body in its movements; or, thirdly, only a portion of the æther is free, the rest being fixed to the molecules of the body and, alone, sharing its movements.

...

I conclude, then, that [the first] hypothesis does not agree with experiment. We shall next see that, on the contrary, the third, or Fresnel's hypothesis, leads to a value of the displacement which differs very little from the result of observation.

...

The success of this experiment must, I think, lead to the adoption of the hypothesis of Fresnel, or at least to that of the law discovered by him, which expresses the relation between the change of velocity and the motion of the body; for although the fact of this law being found to be true constitutes a strong argument in favour of the hypothesis of which it is a mere consequence, yet to many the conception of Fresnel will doubtless still appear both extraordinary and, in some respects, improbable; and before it can be accepted as the expression of the real state of things, additional proofs will be demanded from the physicist, as well as a thorough examination of the subject from the mathematician.

On the Effect of the Motion of a Body upon the Velocity with which it is traversed by Light (1860) Hippolyte Fizeau, Philosophical Magazine, Series 4, vol. 19, pp. 245-260

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  • $\begingroup$ Fizeau would have needed over four significant figures to measure effects in v/c, which seems unlikely on the first try. Can you provide references that back this point up, and account in more detail to what extent his results came into contact with aether theories? $\endgroup$ – Emilio Pisanty Dec 16 '16 at 11:23
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    $\begingroup$ The Wikipedia article has a number of references, including Fizeau's 1851 paper (French) and a 1860 English translation. The required accuracy was achieved through interferometry between two beams travelling through pipes with different water velocities. $\endgroup$ – Sergei Patiakin Dec 16 '16 at 13:20
  • $\begingroup$ Oh, OK. I assumed you meant this one so I didn't click through (but I imagine many others would think the same, so it's maybe worth clarifying). And yeah, if you're doing interferometry you've got oodles of available precision. I make it about a ~1fs resolution in the delay, over a ~1m baseline? Then you'd be able to detect velocity changes as small as one part in a million, or so? $\endgroup$ – Emilio Pisanty Dec 16 '16 at 13:50
  • $\begingroup$ Sergei Patiakin: "Hippolyte Fizeau, Philosophical Magazine, Series 4, vol. 19, pp. 245-260 [ en.wikisource.org/wiki/… ]" -- Thanks for supplying the ready reference. "The Fizeau experiment is a way to measure the speed of light in a moving medium." -- The indicated reference doesn't seem to contain any mentioning of "speed", but (at least) several times of "velocity" and specificly to "the velocity of light in a vacuum". To which definition of this quantity did Fizeau refer specificly? $\endgroup$ – user12262 Dec 18 '16 at 9:34
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This is becoming a little like a list question, but here's another way you can do it without light.

As Emilio Pisanty eloquently describes, there are very strong theoretical grounds, using only symmetry results that intuitive clear to all of us from a very young age (<10years), that there is some, unique, universal signalling speed limit that is also inertial-frame-invariant. We only need to measure this parameter $c$ to find the complete laws. Notice I said "parameter" rather than speed, because we don't needfully have to observe something moving at an inertial-frame-invariant speed to derive $c$ experimentally. This is because the these same arguments give us the full form of the Lorentz transformation (without the actual value of $c$). In particular, they give us the time-dilation factor $\gamma(v)$ as a function of the relative velocity $v$.

So we can use any experiment that observes $\gamma(v,\,c)$ as a function of $v$ and curve fit the experimental results to $\gamma(v,\,c) = 1/\sqrt{1-(v^2/c^2)}$ by adjusting the $c$ parameter for tightest fit of results to the theoretical curve. If our experiments include values of $v$ that are a significant fraction of $c$, then our estimate of $c$ will be a good one.

There is a whole list of experiments that could work in this way.

We could, for example, measure muon decay lifetime measurements $\tau = \tau_0 \,\gamma(v,\,c)$ as a function of $v$.

Or, we could do a lower energy variation on Dmckee's example and measure $v$ as a function of kinetic energy $E = m_o\,c^2 (\gamma(v,\,c) -1 )$ and curve fit this one. We would only have to measure up to about $v=c/2$ (when $\gamma = 1.155$) to get a pretty good estimate of $c$ with modestly accurate equipment.

Of course, the experimental results get better as our technology improves and our experiments access higher and higher speeds.

Eventually they reach the situation described by Dmckee: we simply can't push the particles faster and we're effectively at $c-\epsilon$ speeds, so we can read off $c$ really accurately.

But, supposing we had progressively worked towards better and better experimental results using higher and higher velocities as I described and no-one had ever decided the speed of light were frame-invariant. I should think the estimates one would get at $v=c/4$ (when $\gamma = 1.033$) would, with a large number of repeats and good statistical processing would give an estimate of $c$ accurate enough that someone would say, "Hey, I think I know something that actually moves at the speed parameter $c$"!

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  • $\begingroup$ WetSavannaAnimal aka Rod Vance: "So we can use any experiment that observes $$\gamma[~v, c~] := 1 / \sqrt{1 - (v/c)^2 } $$ as a function of $v$" -- How do (you suppose that) we determine which experiment "observes $\gamma$" (and which doesn't), or for which specific measurement operator(s) the corresponding range of values (which could be obtained by applying the operator to suitable given observational data) ought to be denoted by the parameter $\gamma$ ? Likewise: How do (you suppose that) we determine values of $(v/c)$ from suitable given observational data? $\endgroup$ – user12262 Dec 18 '16 at 10:18
  • $\begingroup$ @user12262 E.g. you look for variations in muon lifetimes with $v$. If you don't see variations, then your $v$ is not high enough - you keep increasing till you do. Likewise, the kinetic energy of a particle is $(\gamma - 1)\,m_0\,c^2$: if this is indistinguishable from $m_0\,v^2/2$, then you keep increasing energy until you do see a difference. Because you know the form of $\gamma$ as a function of $v$ (even though you don't know $c$) from the basic symmetry arguments, you adjust the theoretical curve by adjusting $c$ until it fits your experimental results ... $\endgroup$ – WetSavannaAnimal Dec 18 '16 at 10:53
  • $\begingroup$ @user12262 .... So you're doing a nonlinear regression to estimate $c$ given an experimental curve. $\endgroup$ – WetSavannaAnimal Dec 18 '16 at 10:53
  • $\begingroup$ WetSavannaAnimal aka Rod Vance: "E.g. you look for variations in muon lifetimes with v." -- Fair example; but: How do (you suppose that) we determine "muon lifetimes" (especially as far as that's some quantity other than muon mean life (duration)) and values of "$v$", trail by trial ?? (Not even to mention quantities and/or experiments involving definitions and determinations concerned with dynamics.) $\endgroup$ – user12262 Dec 18 '16 at 11:40
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The strongest current experimental evidence is the standard model of particle physics, the beautiful symmetries of SU(3)xSU(2)xU(1) with the plethora of data that produced them, would fall on their face if c were not the limiting velocity, i.e. if special relativity did not hold.

Every single mass measurement in the particle data book , comes from using energy and momentum conservation equations based on the algebra of the four vectors of special relativity and thousands upon thousands of measured events .

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It is my understanding that the limit is simply asymptotic... as speed increases, so does mass, so increasing speed requires ever increasing energy, to account for the new inertia... eventually the amount of energy needed to accelerate would be infinite, that would the speed limit for all matter/energy anywhere in the universe

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    $\begingroup$ You seem to have answered a different question than the one asked and used an obsolete terminology. People who use relativity day in and day out don't talk about relativistic mass (that is mass that increases with speed) anymore because the conceptual framework is both unnecessary and leads to misapprehensions. $\endgroup$ – dmckee Dec 17 '16 at 5:25
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Without the Michelson-Morley experiment, is there any other reason to think speed of light is the universal speed limit?

The M-M experiment proofs only that the earth's movement is not observable under the rotation of the used interferometer. What is proofed is the time of flight on different paths between light emission point and the observations screen. So the M-M experiment does not proof that the speed of light is the universal speed limit.

The question about the speed limit is answerable in an easy way. Suppose you are the owner of rockets which fly say 6.000 km/h. How do you think to which speed you can accelerate an ant as well as an elephant with such rockets? As long as the empirical facts say that EM radiation has the highest observed speed it could not be found any method to accelerate something to a speed greater the speed of light.

There are some other interesting points:

  1. EM radiation is emitted in packages, called at first quants and later photons. It was proofed that photons with different energy content (of different wavelengths) are traveling in vacuum with exactly the same speed. This was not obvious. It was proofed with very high accuracy and this underlines the existence of the speed of light.
  2. The speed of light is a local value and changes - for an far away observer - with the gravitational potential. Than greater the mass accumulation than slower the light moves. In the space between galaxies with its lower gravitational potential the light moves faster in relation to an observer in an higher gravitational potential.

Anyway the question about other experiments for the proof of the absence of any aether is a very interesting. The M-M experiment has a weakness. Since the gravitational potential has an influence on the speed of light and since gravitational influences the space around the mass it has to be proofed that near the earths surface gravitational does not move the space in the same way as a rotating sphere in a liquid should not influence the liquid. In reality it does.

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    $\begingroup$ Where do you answer the question of which experiments prove the speed of light is the universal speed limit? $\endgroup$ – ACuriousMind Dec 17 '16 at 17:04
  • $\begingroup$ @ACuriousMind Emilio says: "If you wish for an answer inscribed within "experimental physics as of 1888, minus the Michelson-Morley result" then, as I said, the symmetry properties of electromagnetism were plenty to convince Einstein that SR was the right choice." implies that there aren't any other experiments? $\endgroup$ – HolgerFiedler Dec 17 '16 at 18:08
  • $\begingroup$ @HolgerFiedler Precisely: how is "the entirety of experimental electromagnetism", as developed during the nineteenth century, already essentially mature, translate into "there aren't any other experiments"? $\endgroup$ – Emilio Pisanty Dec 17 '16 at 21:29
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Obviously:
The speed of whatever may serve for exchanging signals between participants is necessarily less, or at most as great as, the speed at which the signal front (signal front speed) propagates between them;
provided, of course, a measure of "speed" is defined and applicable at all (which in turn presumes or is at least associated with a suitable measure of "distance", and with a suitable characterization of the relevant participants as a system with geometric relations between each other, a "frame").

The identification of signal front speed $c_0$ with "speed at which electromagnetic wave(form)s propagate in vacuum" is foremost a definition of "vacuum" (in terms of refractive index $n$) and therefore related to how to define refractive index and to measure its values accordingly (where the question arises: did Michelson/Moreley even do that?);
and therefore of practical and historical relevance.

Edit (related to comments): It should be noted that the reasons described above are not derived from any experimental evidence (and therefore contrary to such a presumption expressed in the OP question), but they can and must be considered already in the definition of physical quantities (such as "speed", especially) and therefore already in the design of any possible experiments for measuring "speed".

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    $\begingroup$ How does this answer the question of what other experiments than M-M show that the speed of light is the universal speed limit? $\endgroup$ – ACuriousMind Dec 17 '16 at 17:00
  • $\begingroup$ @ACuriousMind: "How does this answer the question of what other experiments than M-M show that the speed of light is the universal speed limit?" -- The OP question (title and text) does not ask about "experiments that show that [...]" but about "reasons to think that [...]". My answer is aimed at expressing such reasons, and it thereby contradicts the presumption (implicit in the OP question text) that "experimental evidence available at that time" had anything to do with these reasons. (Instead, they relate to exp. design and how to obtain any exp. evidence in the first place.) $\endgroup$ – user12262 Dec 17 '16 at 20:39
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Relativistic effects have been tested (e.g time dialation) and the experiments agree with the theory. Ultimately this means that objects approaching c increase in mass to the point where you will need ever increasing amounts of additional energy to accelerate them further.

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In 1887 (prior to FitzGerald and Lorentz advancing the ad hoc length contraction hypothesis) the Michelson-Morley experiment UNEQUIVOCALLY confirmed the variable speed of light predicted by Newton's emission theory of light and refuted the constant (independent of the speed of the light source) speed of light predicted by the ether theory and in 1905 adopted by Einstein as his second (constant-speed-of-light) postulate:

https://en.wikipedia.org/wiki/Emission_theory "Emission theory, also called emitter theory or ballistic theory of light, was a competing theory for the special theory of relativity, explaining the results of the Michelson–Morley experiment of 1887. [...] The name most often associated with emission theory is Isaac Newton. In his corpuscular theory Newton visualized light "corpuscles" being thrown off from hot bodies at a nominal speed of c with respect to the emitting object, and obeying the usual laws of Newtonian mechanics, and we then expect light to be moving towards us with a speed that is offset by the speed of the distant emitter (c ± v)."

http://philsci-archive.pitt.edu/1743/2/Norton.pdf "The Michelson-Morley experiment is fully compatible with an emission theory of light that CONTRADICTS THE LIGHT POSTULATE."

Banesh Hoffmann, Relativity and Its Roots, p.92: "There are various remarks to be made about this second principle. For instance, if it is so obvious, how could it turn out to be part of a revolution - especially when the first principle is also a natural one? Moreover, if light consists of particles, as Einstein had suggested in his paper submitted just thirteen weeks before this one, the second principle seems absurd: A stone thrown from a speeding train can do far more damage than one thrown from a train at rest; the speed of the particle is not independent of the motion of the object emitting it. And if we take light to consist of particles and assume that these particles obey Newton's laws, they will conform to Newtonian relativity and thus automatically account for the null result of the Michelson-Morley experiment without recourse to contracting lengths, local time, or Lorentz transformations. Yet, as we have seen, Einstein resisted the temptation to account for the null result in terms of particles of light and simple, familiar Newtonian ideas, and introduced as his second postulate something that was more or less obvious when thought of in terms of waves in an ether. If it was so obvious, though, why did he need to state it as a principle? Because, having taken from the idea of light waves in the ether the one aspect that he needed, he declared early in his paper, to quote his own words, that "the introduction of a 'luminiferous ether' will prove to be superfluous."

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    $\begingroup$ This seems to be an attempt to argue that the M-M experiment doesn't show the constancy of the speed of light. While this is in some sense true, I don't see how it answers the question, and I also think answers should contain some original contribution beyond copy-pasting quotes. $\endgroup$ – ACuriousMind Dec 15 '16 at 17:14
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    $\begingroup$ "...the M-M experiment doesn't show the constancy of the speed of light. While this is in some sense true..." In 1887 the experiment PROVED that the speed of light varies with the speed of the source (c'=c+v). But they were all etherists at that time and fabricated, ad hoc, the absurd length contraction - the experiment became "compatible" with what it had originally refuted. $\endgroup$ – Pentcho Valev Dec 15 '16 at 21:29
  • $\begingroup$ He's claiming not merely that M-M doesn't prove constant c, but also that M-M proves variable c. It looks like he's misunderstanding the sources he's quoting, which make only the weaker claim. $\endgroup$ – Thom Smith Dec 16 '16 at 18:13
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    $\begingroup$ @PentchoValev Claiming that light is moving with the speed of plus the speed of the source is wrong. Would it be so we should observe in particle accelerators EM radiation with near twice the speed of light. Saying that light moves with c and see depends locally from the gravitational potential would not contradict the M-M-experiment. $\endgroup$ – HolgerFiedler Dec 17 '16 at 7:36

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