Would it be possible to develop special relativity without knowing about light?

Question

My understanding of special relativity is that it is fundamentally based on the constancy of the speed of electromagnetic radiation - that this speed is a physical law (or derivable from physical laws and facts about the vacuum) and not a contingent fact. Does that mean that, if humanity did not know about light (or electromagnetic radiation, generally), would we then be unable to come up with special relativity? To put it another way, imagine a species of intelligent life insensitive to electromagnetic radiation - no eyes etc. Would they still have a reason to produce the theory of relativity, or would they likely have created a physics framework which doesn't involve the speed of light so centrally?

Answer 1

It is, in fact, possible to derive the mathematics of the theory of relativity without reference to light. David Mermin did so in 1984 (Mermin N D 1984 Relativity without light Am. J. Phys. 52.2 119–24). According to the abstract, "The relativistic addition law for parallel velocities is derived directly from the principle of relativity and a few simple assumptions of smoothness and symmetry, without making use of the principle of the constancy of the velocity of light."

So, being insensitive to electromagnetic radiation does not preclude the derivation of relativity, although the lack of a speed-of-light-centered theory (depending on how you define this) is still an open question. c might just mean something conceptually different to them, but it'll still show up.

Answer 2

My understanding of special relativity is that it is fundamentally based on the constancy of the speed of electromagnetic radiation

Actually, no, that's true. Special relativity is (one could say) based on the existence of some speed that is invariant in all inertial reference frames. The fact that light (or anything else) travels at that speed is pretty much irrelevant. So while the development of SR was originally prompted by the constancy of the speed of light, it's not a requirement to have developed the theory. The effects of relativity would become apparent just from the time dilation/length contraction experienced by any sufficiently fast-moving object.

Answer 3

Relativity without light:

http://ajp.aapt.org/resource/1/ajpias/v52/i2/p119_s1?isAuthorized=no

Abstract: The relativistic addition law for parallel velocities is derived directly from the principle of relativity and a few simple assumptions of smoothness and symmetry, without making use of the principle of the constancy of the velocity of light.

There is also a chapter devoted to this topic in this book: http://ebooks.cambridge.org/chapter.jsf?bid=CBO9780511608216&cid=CBO9780511608216A028

Note that I do not have access to either of those sources, although the OP may do, or he/she may wish to obtain such access.

Here is a free article on the related subject: http://image.sciencenet.cn/olddata/kexue.com.cn/upload/blog/file/2010/8/201085162128290613.pdf and its abstract:

The role of the light postulate in special relativity is reexamined. The existing theory of relativity without light shows that one can deduce Lorentz-like transformations with an undetermined invariant speed, based on homogeneity of space and time, isotropy of space and the principle of relativity...

Another free article, this one courtesy of CERN: http://cdsweb.cern.ch/record/940058/ and its abstract:

Using only the reciprocity postulate, it is demonstrated that the spatial separation of two objects, at rest in some inertial frame, is invariant. This result holds in both Galilean and special relativity. A corollary is that there are no `length contraction' or associated 'relativity of simultaneity' effects in the latter theory. A thought experiment employing four unsynchronised clocks and a single measuring rod provides a demonstration of the time dilatation effect. This effect, which is universal for all synchronised clocks at rest in any inertial frame, is the unique space-time phenomenon discriminating Galilean and special relativity.

Answer 4

Albert Einstein was largely motivated by Maxwell's equations and the electromotive force in particular. So it would be quite possible to develop special relativity without the special case of light. Amphere's law is a relativistic effect, so that would be enough.

Answer 5

What if Bats indeed would have been intelligent? :)

Think about it like that: Any changes requires signal trasmission of ANY kind (in bats case sound in the air). There are 2 cases:

1) Signal trasmission is infinitely fast - in this case we get Galileo-Newton mechanics.

2) Signal trasmission is finite - in this case we have SR.

What is signal? Signal is a general process(phenomenon) by which far world ALIENS determine such conceptions as SPEED, TIME and so on (we use light for everything). If they dont have these conceptions then we are in trouble and we can not asnwer your question casue WE DONT KNOW, but if there is some sort of speed and time variables in their physics picture then they will rediscover special relativity.

Answer 6

No, it wouldn't be possible to develop special relativity without light. Scientists developed a model of the propagation of light in a material substance called the ether based upon what they knew about the propagation of sound waves in a medium. Their expectation was they would be able to detect the speed at which the Earth travelled through it, but experiments gave a null result which scientists found initially confusing. Eventually this gave birth to the Special Theory of Relativity.

You therefore need to know about light behaving differently to what you know about sound, to see there is something interesting going on.