Why is there a C? - Exploring the Singularities of Fixed Speed

[AlecsSmart]

I was talking to Galileo the other day and he told me that motion is relative. A ship is moving relative to the shore and vice versa, and so is everything else in the universe. Nowadays you wouldn't dream of fixing all positions and motion to one universal reference point. Physics should work from anywhere. Nobody can say that anyone object is fixed in place.

So now I want to measure how fast I can ride my bicycle. By that I mean, what is it faster than, and what is it slower than. Surely I should be able to measure that against anything I want? Surely nobody can say that the speed of anything is fixed? Apparently not, speed is not like position, there is a fixed speed C. Why do you fix the speed of one phenomena, when you wouldn't fix the position of anyone thing?

By fixing a speed you are fixing the definition of space. A metre is a fraction of the distance light travels in a second. So I can't describe how long something is against anything I want, like I would with motion, instead I have to use the fixed C. Surely the length of something should be like the position of something; anything can move, why can't anything grow?

In my own private universe I have a spring and a balloon. All motion is relative, but here so is all length. If I fix length to the spring, then I can investigate the inflation of the balloon when I puff air into it. Now look what happens when I compress the spring. Nothing happens to the length of the spring, but the balloon looks like it is expanding, or 'space itself' is expanding. This is absurd.

In this universe, why can't I use Bee instead of C? A standard measure would be a fraction of the distance the bee travels in a second. Then I can use that to calculate how fast I cycle (I'm slower uphill than I am downhill). I should also be able to use the constant speed of my cycling to measure the length of anything. Surely speed, length, and time are as relative as position. Only they're not in relativity, you use C. What excuse does relativity have for violating the 'measurements are relative' principle?

Funny things happen when you fix a speed. If I measure a tree branch by riding past it, and knowing that the speed of my cycling is constant, I will find that it seems shorter when lying on a downhill slope. My speed is fixed, so space itself is warped around hills. How long is a tree trunk? You're going to be waiting forever for my to ride vertically. So...speed of cycling times infinity...the tree is infinitely high. Doesn't fixing C to a single phenomenon lead to singularities? If so, what excuse do you have for holding on to this luminocentric view of the universe?

From my perspective, the theory of relativity is just the limited case where spacetime is always measured against the speed of one fixed phenomena among many. Sure, some things are 'more constant' than others, and Einstein's C is more constant that my Bee. But that is not a good reason to keep C, because the Earth is more fixed in place than my bee as well, but that doesn't stop me, in principle, from using the bee as a reference frame.

There are situations where the current version of relativity doesn't work, in singularities. I get the same problems using Bee. If space is defined with reference to the speed of Bee, and, relative to other things, the bee stops, then space has no meaning there. Surely this can happen with whatever you choose to fix the speed of. I can see one way of avoiding singularities, and that is by not fixing the speed of anything.

When I asked another 'expert' about this, I was told 'we looked, and saw that light traveled at C'. But that is not a good excuse. He could have said that he observed that the Earth was fixed, and would have been just as right.

Here is one possible way, for instance, to interpret a couple of observations differently to the usual relativistic way...

Start with some axioms. I'm going to use Euclid's geometric axioms to describe the universe, so one thing I know by postulate is that space is flat. Einstein used C to figure out that gravity warps space-time, and Euclidean space can't warp, so I'll use a bit of symmetry to figure that gravity determines the speed of light (skipping over subtleties of working). Speed is distance over time, when speed was fixed space-time warped, now they're fixed so speed (in this case of light) must move. So on top of Euclid's geometry, we have light determined by gravity, two axioms.

Now when Michaelson and Morley try to measure changes in the speed of light they're not going to see any by comparing both light sources in the same gravity field, as the gravity there will determine the speed of them both. So light speed isn't the same for any observer. A second relativistic effect is gravitational lensing. If Michaelson and Morley look up they might observe light slowing down and speeding up as it flows past massive bodies, going into higher and lower gravitational fields. But as they imagine light to be waves, they're not going to be surprised when it refracts.

So using Euclidean space, Newtonian gravity and Snell's law for refraction, I could 'explain' a couple of observations used to support relativity, without singularities. So why would you make spacetime bend to accommodate a fixed C?

 

[Hurkyl]

So using Euclidean space, Newtonian gravity and Snell's law for refraction, I could 'explain' a couple of observations used to support relativity,

Have you tried it?

 

[atyy]

By fixing a speed you are fixing the definition of space.

Yes, more or less, you fix the definition of spacetime. So modern special relativity says there is a fixed spacetime metric, the Minkowski metric. The symmetries of the laws of physics with respect to this metric are the reason we can define a class of preferred coordinate systems called Lorentz inertial frames in which the laws of physics look the same no matter which Lorentz inertial frame you choose.

 

[Bob S]

Have you ever met Mr. Tompkins? He was a banker who, after attending several lectures on relativity and quantum mechanics, decided to set c = 10 kilometers per hour. Read about his recount of the experience here:

http://boomeria.org/physicslectures/secondsemester/relativity/tompkins.html

Bob S

 

[Hurkyl]

By the way, do you realize there is a theory in which the relationship between space and time is Galilean, but it makes exactly the same predictions as special relativity? Despite this, we prefer the Minkowski geometry of special relativity. Do you know why?

 

[AlecsSmart]

we prefer the Minkowski geometry of special relativity. Do you know why?

No. I haven't met Mr Tompkins and I don't know why you prefer Minkowski geometry. Mr Tompkins still appears to have C, just a different C. Hurkyl's response is cryptic.

 

[russ_watters]

Now when Michaelson and Morley try to measure changes in the speed of light they're not going to see any by comparing both light sources in the same gravity field, as the gravity there will determine the speed of them both.

Gravity determines the speed of light? Where did you get that idea?

 

[bcrowell]

Why do you fix the speed of one phenomena, when you wouldn't fix the position of anyone thing?

This is a very good and natural question. In 1905, when Einstein formulated special relativity, there was only one known fundamental field, the electromagnetic field, so singling it out for special treatment was not so obviously the wrong thing to do. From a modern point of view, c should be considered as a conversion factor between space and time units, not the speed of light.

FAQ: Is the c in relativity the speed of light?

Not really. The modern way of looking at this is that c is the maximum speed of cause and effect. Einstein originally worked out special relativity from a set of postulates that assumed a constant speed of light, but from a modern point of view that isn't the most logical foundation, because light is just one particular classical field -- it just happened to be the only classical field theory that was known at the time. For derivations of the Lorentz transformation that don't take a constant c as a postulate, see, e.g., Morin or Rindler.

One way of seeing that it's not fundamentally right to think of relativity's c as the speed of light is that we don't even know for sure that light travels at c. We used to think that neutrinos traveled at c, but then we found out that they had nonvanishing rest masses, so they must travel at less than c. The same could happen with the photon; see Lakes (1998).

Morin, Introduction to Classical Mechanics, Cambridge, 1st ed., 2008

Rindler, Essential Relativity: Special, General, and Cosmological, 1979, p. 51

R.S. Lakes, "Experimental limits on the photon mass and cosmic magnetic vector potential", Physical Review Letters 80 (1998) 1826, http://silver.neep.wisc.edu/~lakes/mu.html

 

[Hurkyl]

No. I haven't met Mr Tompkins and I don't know why you prefer Minkowski geometry. Mr Tompkins still appears to have C, just a different C. Hurkyl's response is cryptic.

(Incoming analogy warning)

Imagine that we have an interesting device which rolls a die in secret. We have another device that peeks into the first device to see what number is rolled, adds something to it to make it 7, then displays the result.


Now you, as a user of these two devices have a choice: you can think of the second device as doing an observation, a calculation, then displaying the result, or you can think of it as simply printing 7 all of the time.

Presumably, you would pick the latter!


Of course, you have another course of action -- you could actually break open the first device so that we can directly observe the die, and analyze the circuitry of the second device, and check that it really does what I said above. (Or, you might find out that everything I said is a lie, and I just gave you a device that prints 7 whenever you ask it to print something)



Now, on the other side of the analogy, the ether theory has a Galilean space-time, but all measurement is done through laws of physics that add extra terms to make everything look Minkowski.

e.g. are you chasing after a light beam? Your rulers get contracted and your time dilates so you measure its speed as c, rather than something less! (Note that, in this ether theory, contraction and dilation are, in principle, absolute notions)

Unlike the first part of the analogy, we do not have the option of peeking under the hood -- there is no law of physics that let's us tell when two things are simultaneous, or to make measurements of absolute time or absolute position.

So, we're faced with the two choices: we can think of space-time as being Galilean but all of our measuring devices conspire to produce Minkowski results... or we can think of space-time as being Minkowski.

So, we think of space-time as Minkowski.


"But wait!" you might say, "aren't there conceptual advantages to having a theory with an underlying Galilean universe, even if we can't see it?" IMO there isn't, but that's a moot point because we have the following:

The study of Minkowski geometry let's us pick coordinate charts relative to which we can do measurements and calculations and stuff. So if there is any conceptual advantage to thinking in terms of a Galilean space-time, we can simply choose a convenient inertial reference frame, look at its Galilean boosts (which won't be inertial, but they are still coordinate charts), and do all the Galilean + ether theory analysis we want.

 

[James S Saint]

The propagation of affect (the "speed of light") is what determines the size, time, and distance of all things, hence their measured velocities (dx/dt). That is why it is the "chosen one".

If you could magically double the speed of affect, the entire universe would merely double in size and you would not be able to know the difference.

The value of c is finite because it is impossible for any existence to be infinite (by definition). But also any affect must only affect its adjacency and thus to affect anything else, it must "travel" through all other affects. Thus propagation is born with a finite speed. All other speed and distance is then measured from it.

On the other hand, if you were to double the speed of all bees, I suspect you would do no more than get some people and the ecology really upset.

 

[Austin0]

(Incoming analogy warning)

Now, on the other side of the analogy, the ether theory has a Galilean space-time, but all measurement is done through laws of physics that add extra terms to make everything look Minkowski.

e.g. are you chasing after a light beam? Your rulers get contracted and your time dilates so you measure its speed as c, rather than something less! (Note that, in this ether theory, contraction and dilation are, in principle, absolute notions)
.

I am just curious as I have not studied the ether theory.
How does contraction and dilation, even if absolute, possibly explain the isotropic invariance of c. Specifically measurements with and against the path of motion?
Thanks

 

[Saw]

I am just curious as I have not studied the ether theory.
How does contraction and dilation, even if absolute, possibly explain the isotropic invariance of c. Specifically measurements with and against the path of motion?
Thanks

In Lorentz Aether Theory (LET), it'd be said that a ship 1 that has been accelerated to speed v1 wrt the Aether suffers absolute length contraction, in the sense that if the ship's ends are compared with those of another ship 2 accelerated to a (lower) v2 and this comparison is made for the two ends simultaneously and this simultaneity is also the absolute one, that is to say, the one measured in the Aether frame, ship 1 will be shorter, because it is moving more quickly wrt the Aether. However, LET admits that you cannot determine which frame is at rest wrt the Aether, because all what you can measure is relative time lapses, length and simultaneity. So you content yourself with the relative concepts and of course, then, you also measure c for light in all directions, due to a compensation of effects that conspires to this effect. Difference with SR? Tricky subject. In my opinion, between Lorent and Einstein there was no disagreement at all and they did not see their theories as distinct. Einstein said, "we do not need the aether" and Lorentz more or less replied, "well, that is true, after all, and it is quite practical; the aether may exist or not, it may have these or other features but as long as no problem requires it, we do not need to waste time on that issue... "

 

[James S Saint]

Einstein said, "we do not need the aether" and Lorentz more or less replied, "well, that is true, after all, and it is quite practical; the aether may exist or not, it may have these or other features but as long as no problem requires it, we do not need to waste time on that issue... "

Very true, but now we DO have "problems" requiring its recognition. Sad that so many have emotion issues against it.

 

[AlecsSmart]

Gravity determines the speed of light? Where did you get that idea?

I assumed that in general relativity, when you see light bending around massive bodies, it means spacetime is warped by gravity, because the light is traveling at c. I swapped a couple of postulates, I allowed light to change speed by getting rid of c, fixed space as flat Euclidean style and did the equivalent thing with time, then balanced the equations. Spacetime can't change with gravity, observations stay the same, it must have been light speed changing with gravity.

From a modern point of view, c should be considered as a conversion factor between space and time units, not the speed of light.

FAQ: Is the c in relativity the speed of light?

This is not the right answer. Whether c is a conversion factor between space and time units or the speed of bee, you still have c. Whatever it represents is not the main issue. I blamed c for causing singularities. I claimed some observations of light could be explained without c, assuming light was one of the things that traveled at c (provisos excepted). Relativity still has c, whatever it represents, and still has singularities. Either I am wrong to claim that these observations can be explained without and c, or I am wrong to blame singularities on c, or there is some good reason for keeping c that the physics community knows about and I don't.

 

[Fredrik]

I assumed that in general relativity, when you see light bending around massive bodies, it means spacetime is warped by gravity, because the light is traveling at c.

You could say that spacetime is warped by the matter in it. That warping is gravity (in general relativity). The last part about light is just wrong.

I swapped a couple of postulates, I allowed light to change speed by getting rid of c, fixed space as flat Euclidean style and did the equivalent thing with time, then balanced the equations. Spacetime can't change with gravity, observations stay the same, it must have been light speed changing with gravity.

This site has rules against personal speculation.

...some good reason for keeping c that the physics community knows about and I don't.

The invariance of the speed of light is a part of the definition of both SR and GR. Experiments have proved a) that SR makes much better predictions about results of experiments than prerelativistic theories of space, time and motion, and b) that GR makes much better predictions that SR.

 

[AlecsSmart]

The last part about light is just wrong.

OK, I said the wrong thing there. I was trying to say was, c causes singularities. I still believe this to be the case. You have said you don't like analogies, so instead I have provided a thought experiment.

Get on your bicycle and follow me as we cycle around One Tree Hill. Try and keep up. To count units of time, I am going to use the point when the right pedal is closest to the ground. A unit of time is the time between these two events. To measure space I am going to mark a place on the back tyre. The space between where this mark hits the ground on two occasions is a unit of space. You can consider c as a conversion factor between time and space units, or in this case a conversion factor between pedals and wheels. Change gears. Now you have more time units for less space or vice versa. As we cycle along together in different gears, there is still a constant c, so we're allowed you to change pace.

Keep cycling around the hill and watch me as I ride to the top. When we were riding together, whatever gear we were in, our pedals, or time counters, were in some way synchronised. But now as I ride up the hill that it is not so easy for me to keep up the pace. However, we have a c, so we have to say that I would always keep up with you. From your perspective I'm traveling through a time warp, because my units no longer mesh with your units. The tree at the top is a singularity, where the warp is so extreme that a unit of time takes forever.

If you don't like this thought experiment I have others. Try your own. The way I see it, any c can introduce singularities, so using them is a measurement error. I'm not the first to point out that singularities defy logic. What would I need to do to convince you that the relativistic approach is not sound? (This is not the same as not valid in deductive reasoning).

SR makes much better predictions about results of experiments than prerelativistic theories of space, time and motion.

If pre-relativistic theories didn't predict the correct results, this doesn't mean their theories of space, time and motion were wrong. There is always a symmetric way of describing results. For example, either length contracted or something got shorter, time dilated or something slowed down. All measurements are relative. Have you tried fixing space-time and looking back at relativistic evidence? You might find something interesting about things that exist in that space-time, rather than about space-time itself.

I made a singularity by adding c to a couple of bicycles, and assumed it was similar to the way you made black holes. If I did something wrong when making my singularities, then how do you make your's?

 

[Naty1]

Why is there a C?

I presume you mean by this why is there a fixed speed of light...unlike other phenomena. Good question, but "why" questions soon run up against the current limits of science. Nobody knows why the speed of light is fixed while space and time are variables.

Prior to Einstein, many thought just about the reverse was true. So an equivalent question would be "why are space and time variable?" Nobody knows why all the other "constants" of the Standard Model of Part cle Physics, such as the charge of the electron, are what they are either...they are all experimentally determined. (There are prior threads here discusing this.)

If the speed of light were different, but fixed, as BobS posted above, things would be different but potentially very viable...not at 10m/s though. We could exist and make sense of things in many situations such as a fixed speed of light at c +/-1 m/s instead of c.

I did not read the whole Mr Tompkins story, but if the speed of light varied significantly from "c", electromagnetic forces holding atoms together, as well as all other forces (strong, weak, gravitational) would in all probabilty lead to a very different universe...or no universe at all...almost certainly a universe without us present to ask questions. To form planets, galaxies, atoms, etc, many "constants" need to be fairly fine tuned (close to their measured values) for us to exist as we do.

On the other hand, if C varied, willy nilly or significantly over time or say varied with distance, cause and effect could be REALLY confusing...maybe impossible to decipher...and again our universe would most probably not even exist.