Must measurement of time reference light?

[mdeng]

My question is about time-space. It seems to me that special relativity measures time based on light and derives its conclusion on that base. If my understanding is correct, why should we rely on light to measure two moving clocks? Must we involve light when talking about time? What if light has some "strange" property which would distort our result? Granted, relativity theories provide good answers to the world where time difference is being measured using light. But it seems to me there must exist another world that is more intrinsic and where time may be measured with a superior means. This world might give us
better insight to the "strange" property of light and may reveal that space-time might no
longer be tied together. Is there any work on this subject?

Thanks,
- Ming

 

[Riogho]

The speed of light in a vacuum is constant. That is 'c'.

Why would it be bad at all to measure something off of a constant?'

Galileo used his pulse to measure time at the beginning of his experiments, then he realized that his pulse was not a constant. Therefore he invented clocks using falling water, which, thanks to gravity. Is a Constant. (Or close enough for his means)

So we use the only constant we know, the speed of light.

Do you have any better ideas?

 

[mdeng]

The speed of light in a vacuum is constant. That is 'c'.

Why would it be bad at all to measure something off of a constant?'

My question is not about its goodness or badness, but about whether time-space relativity is something intrinsic to the physical property of time and space. Perhaps, if we look beyond light, time and space will both be constant. But even that (being constant or not) is not my question. The question is whether there is something beyond light we can use to talk about about time and space and what it might reveal.

Galileo used his pulse to measure time at the beginning of his experiments, then he realized that his pulse was not a constant. Therefore he invented clocks using falling water, which, thanks to gravity. Is a Constant. (Or close enough for his means)

So we use the only constant we know, the speed of light.

My question is not about what we use as a yard stick to measure time-space in either theoretical or practical way. Rather, it is about what we may discover if we don't involve light when studying moving clocks. We might come to a conclusion different from the time-space relativity. My underlying question is why light has a constant speed and its consequence derived by Einstein. This the relativity theory does not explain. I strongly believe that something must be happening to light, based on the cause-and-effect law in classical physics. In this regard, the relativity theory seems to be missing some parameters.

 

[Riogho]

To begin, here are our assumptions, some of which are generic in nature, while others are specifically about electricity and magnetism. First, the generic ones:

Space is homogeneous. The equations of physics work the same in New York and Los Angeles, on Earth or on Mars, in the Milky Way or in the Andromeda Galaxy.
Space is isotropic. The equations of physics don't change just because you turn around and look in a different direction.
Space is symmetric under time translation. The equations of physics are the same today as they were yesterday, and as they will be tomorrow.
Space is symmetric under a "boost". The equations of physics work the same in moving coordinate systems: your pocket watch, computer, or your body for that matter won't cease to function just because you're moving on a train, an airplane, or spacecraft .
The specific assumptions about electricity and magnetism are the culmination of 100 years of research and experiment, and were first put into modern form by Maxwell in the 1860s. In plain English, this is what they say:

The sum total of the electric field around a volume of space is proportional to the charges contained within.
The sum total of the magnetic field around a volume of space is always zero, indicating that there are no magnetic charges (monopoles). (With a bar magnet, the number of field lines "going in" and those "going out" cancel each other out exactly, so there is no deficit that would show up as a net magnetic charge.)
A change over time in the electric field or a movement of electric charges (current) induces a proportional vorticity in the magnetic field.
A change over time in the magnetic field induces a proportional vorticity in the electric field, but in the opposite direction.
These four assumptions can also be stated exactly using mathematical language: specifically, the language of vector calculus. But before we continue, it is important to make note of the fact that we are done with the assumptions: what follows is rigorous logic. In other words, if one wishes to argue that Einstein's conclusion is wrong, one either has to throw logic out the window, or find fault in one or more of the assumptions above.
To examine the speed of light in free space, we can simplify two of our assumptions. In free space there are no charged bodies or particles about, and therefore Maxwell's first assumption reads as:
The sum total of the electric field around a volume of empty space is zero, indicating there is no electric charge contained within.
Similarly, we can drop the bit about electric current from the third assumption:
A change over time in the electric field in empty space induces a proportional vorticity in the magnetic field

 

[Riogho]

Mathematically, the first two assumptions are expressed through the concept of divergence. If we imagine the electric field with lines of force, as in a high-school physics textbook, divergence basically tells us how the lines are "spreading out". For the lines to spread out, there must be something, intuitively speaking, to "fill the gaps": these things would be particles of charge. But there are no such things in empty space, so we can say that the divergence of the electric field in empty space is identically zero:


div E = 0.

The electric field is a vector field: the force it produces has a strength as well as a direction. The divergence of a vector field in a given coordinate system is computed through partial derivatives of the vector components:

div v = ∂vx + ∂vy + ∂vz
∂x ∂y ∂z

So far so good. What we said about the electric field also applies to the magnetic field of course:

What about the vorticity? The vorticity of a vector field is also computed through partial derivatives:

curl v = ┌

∂vz – ∂vy
∂y ∂z

∂vx – ∂vz
∂z ∂x

∂vy – ∂vx
∂x ∂y



Unlike the divergence of a vector field, which is a number field (called a scalar field), the vorticity of a vector field is another vector field. Intuitively what it means is that a vortex not only has strength, but it also has an axis pointing in a specific direction.

In this mathematical formalism, the second pair of Maxwell's equations in empty space can be expressed as:


curl B = ∂E/∂t, and



curl E = –∂B/∂t.

To further simplify calculations, we'll assume that the field depends only on one spatial coordinate, say, x. Feynman offers the example of a large (infinite?) charged sheet in the y-z plane that moves in a direction perpendicular to its surface as a source of this field. The same computation can be performed in the general case, but it is a lot more complicated (and a lot less instructive.)

In this case, the first pair of Maxwell's equations tells us that Ex and Bx must be constant functions.

The second pair of Maxwell's equations reduces to the following simple set:

– ∂Bz = ∂Ey
∂x ∂t

∂By = ∂Ez
∂x ∂t

– ∂Ez = – ∂By
∂x ∂t

∂Ey = – ∂Bz .
∂x ∂t


Using the first and the fourth equation, for instance, we can find a solution for Bz (or Ey). Consider:

– ∂2Bz = ∂2Ey .
∂x2 ∂x∂t

and

– ∂2Bz = ∂2Ey ,
∂t2 ∂x∂t

or

∂2Bz – ∂2Bz = 0.
∂t2 ∂x2

This can be rewritten as:

∂ – ∂
∂ + ∂
Bz = 0.
∂t ∂x ∂t ∂x

Solutions to this equation can be found in the form:

Bz = f1(t – x) + f2(t + x),

where f1 and f2 are arbitrary functions. The same solution exists for By, Ey, and Ez.

If we set f2 = 0, then

Bz = f1(t – x),

which is a legitimate solution to Maxwell's equations. What this means is that if the field has a certain value at t = 0, x = 0, then it'll have the same value at t = t0, x = t0. Similarly, if we set f1 = 0, a field that has a certain value at t = 0, x = 0, then it'll have the same value at t = t0, x = –t0. Thus we can say that the electromagnetic field represented by this solution is moving at unit velocity along the x-axis in either of two directions.

So what's this unit velocity business? Though it was perhaps not evident, in the derivation so far we made no attempt to use units of measure that are commonly used in engineering. This is quite legitimate, since different units of measure would only introduce constant multipliers that leave the structure of the equations unchanged. Had we used SI units throughout, we'd have found the final result appear only slightly different:

Bz = f1(ct – x).

Our choice of units (or no units, as the case might be) simply meant that we chose to have the constant c = 1. Using another set of units, e.g., SI units, we might find that c is equal to something else, such as 299,792.5 km/s.

What is important to realize is that regardless of what units we choose, the observed speed will be the same to all observers. Same regardless of where they are. Regardless of when they make their measurements. Regardless of how fast they themselves are moving, and in which direction they are facing. Whether you move towards a light source or away from it, the speed appears the same.

This of course makes no sense in ordinary Euclidean spacetime: when you are running ahead of a moving train, it'll appear slower (i.e., take longer to hit you) than when you're running towards it.

Special relativity is simply the most economical way to solve this dilemma. The idea is to find the simplest geometry in which all our initial assumptions can be simultaneously true.

Why geometry? If you think about it, when you switch from a stationary coordinate system to a moving one (i.e., from a coordinate system fixed to the clock of a railway station to one that is fixed to the main axis of your steam engine) it's really just a simple coordinate transformation: t' = t, x' = x – vt. And herein lies the problem: after this coordinate transformation, in the new coordinate system a ray of light no longer satisfies the conditions that we derived previously. If, in the old coordinate system, an electromagnetic field had the same value at t = 0, x = 0 and t = t0, x = t0, in the new coordinate system, it'll have the same values at t' = 0, x' = 0 and t' = t0, x' = t0 – vt0, and this contradicts what we just learned about Maxwell's equations as x' won't be equal to t'.

The simple geometry of special relativity, Minkowski spacetime, is built around the assumption that the quantity dt2 – dx2 – dy2 – dz2 remains constant under a "boost", i.e., when you change from one moving coordinate system to another. In our simple scenario with only one spatial coordinate, this reduces to dt2 – dx2 remaining constant when you switch from a stationary to a moving system. For rays of light moving in either direction, dt2 – dx2 remains 0 regardless whether you measure it from a moving or stationary system, which is precisely what we want in order to remain consistent with Maxwell's equations..

This assumption leads to a new form of coordinate transformation, the Lorentz transformation. To see why, compare the values for the station and the train in the diagram above. For the station, dt = t0, dx = x0 = vt0 (this, after all, is how we define the train's velocity v) and therefore, dt2 – dx2 is t02 – v2t02. For the train, dx' = 0 and thus dt'2 – dx'2 is t'02. We want the values for the station and the train to be equal:

t'02 = t02 – v2t02
t'02 = t02(1 – v2)
t0' = t0√(1 – v²)

And this, of course, is the fabled Lorentz transform.

Any other approach would either have to use a more complicated geometry (the late 19th century concept of "ether" can be viewed as an attempt to do just this) or it would require giving up at least some of our initial assumptions. And what's wrong with that, you ask? Well, those assumptions are supported by an enormous number of physical observations, not the least of which is the observation that this computer in front of me is functioning as expected, even though it is moving about at a not altogether inconsiderable velocity as the Earth spins, moves around the Sun and, along with the Sun, moves about in the Universe...

 

[Dale]

It seems to me that special relativity measures time based on light and derives its conclusion on that base. If my understanding is correct, why should we rely on light to measure two moving clocks? Must we involve light when talking about time?

Hi Ming, my guess is that you are referring to the idea of a "light clock" that is commonly used as a "thought experiment" in order to geometrically derive time dilation. This light-clock idea is used because it is easy to understand and analyze, but it is not a necessary idea.

Basically, if there is a finite speed which is invariant and if there is no preferred state of inertial motion then the Lorentz transform follows. The properties of time dilation, length contraction, relativity of simultaneity, etc. are all properties of the Lorentz transform. The constant, c, is this finite invariant speed.

It may be that photons have some very small mass. If so, then the speed of light would be slightly different from the invariant speed, c. This would require some serious rewording of textbooks, but the experimental basis supporting the Lorentz transform would still be intact.

 

[mdeng]

Riogho, I am not at all arguing that Einstein is wrong. His theory no doubt provides a great tool to work with the physical world as we know it. However, I wonder that if we use something other than light when discussing about time, perhaps we may come to a conclusion that extends relativity theory just as the way relativity theory extends Newton’s laws. Like you said, “Special relativity is simply the most economical way to solve this dilemma. The idea is to find the simplest geometry in which all our initial assumptions can be simultaneously true”, there may be some not-so-economical way to do it which goes beyond light and offers a more universal equation.

And thanks about giving an intuitive interpretation of Maxwell’s equation. One thing I kept wondering is what the intuition is about the invariance of speed of light, a byproduct of Maxwell’s equation.

 

[mdeng]

DaleSpam and Riogho,

Just read some on Lorentz transform at wikipedia. I found there the following statement interesting.

http://en.wikipedia.org/wiki/Lorentz_transformation][/PLAIN]
The usual treatment (e.g. Einstein's original work) is based on the invariance
of the speed of light. However, this must not necessarily be the starting
point: indeed (as is exposed, for example, in the second volume of the Course
in Theoretical Physics by Landau and Lif****z), what is really at stake is the
locality of interactions: one supposes that the influence that one particle,
say, exerts on another can not be transmitted instantaneously. Hence, there
exists a theoretical maximal speed of information transmission which must be
invariant , and it turns out that this speed coincides with the speed
of light in the vacuum. It is interesting to know that the need for locality
in physical theories was already seen by Newton (see Koestler's "The
Sleepwalkers"), who considered "philosophically absurd" the notion of an
action at a distance and believed that gravity must be transmitted by an agent
(interstellar aether) which obeys certain physical laws.

In an 1964 paper,[12] Erik Christopher Zeeman showed that a, in a mathematical
sense, weaker condition, the causality preserving property, is enough to
assure that the coordinate transformations be the Lorentz-transformations.

The mention of “locality of interaction” above is interesting, and I guess that is what DaleSpam was referring to as well. I can sort of see it true “there
exists a theoretical maximal speed of information transmission which must be
invariant”, though a mathematical proof would satisfy me better. If indeed “this speed coincides with the speed of light in the vacuum”, then I can understand that we must involve light or its equivalent when discussing about time, motion, locality, etc. But I’ll continue to wonder why light possesses this peculiarity, and what it really means to apply velocity addition to light, or what happens for something whose speed is close to light and the addition of their speeds is greater than c.

 

[Dale]

I can sort of see it true “there
exists a theoretical maximal speed of information transmission which must be
invariant”, though a mathematical proof would satisfy me better.

This is never proven in SR, it is assumed as a postulate. However, the resulting experimental predictions are very accurate so it is considered an experimentally verified postulate.

By the way. Although the light clock is frequently used in SR thought experiments the definition of a second is not referenced to the speed of light. (Although the definition of a meter is).

 

[CJames]

The perception of time has to be tied to the speed of light. For example, light has a frequency of so many waves per second. If something is moving away from you, it is redshifted, so you see fewer waves per second. Say a spaceship moves away from you at close to the speed of light carrying a plain old mechanical clock. Light emitted from that clock is going to send out a certain number of waves each time it ticks. If we look at that clock w/ a telescope the light coming from that clock will be redshifted so that there is more time between the waves. That doesn't change the fact that their were only so many waves between ticks of the clock, so the ticks of that plain old mechanical clock will appear slower.

Now of course on its way back, the light will be blueshifted, and the clock on the spaceship will actually appear to be ticking faster than ours. In total, though, it works out mathematically to be more ticks for the moving clock. The standard time dilation equation is in terms of a round trip, or for a clock moving perpendicular to our line of vision.

 

[GODISMYSHADOW]

Einstein only said, "time is what a clock measures." He would not allow himself to be drawn into a philosophical argument. When the Michelson–Morley experiment failed to detect an ether wind, physicists set about trying to explain it. Lorentz tried to explain things his way, and came up with the length contraction equation, but he still believed there was an ether. Einstein had his own thoughts. He postulated that as long as the observer is in an inertial reference frame, when he tries to measure the speed of light he will always come up with the same number. Using this postulate and a little algebra, he discovered he could crank out Lorentz' length contraction equation, without believing in the ether. His ideas about space-time were a development of Minkowski's ideas.

 

[Dale]

Now of course on its way back, the light will be blueshifted, and the clock on the spaceship will actually appear to be ticking faster than ours. In total, though, it works out mathematically to be more ticks for the moving clock. The standard time dilation equation is in terms of a round trip, or for a clock moving perpendicular to our line of vision.

None of the relativity effects are due to appearances. Everything is done by taking into account the finite time required for the propagation of light. A moving clock actually ticks slower than a stationary clock regardless of the direction of travel. It is not merely an optical illusion.

Your Doppler example is also a little confused. Yes, light from a source moving towards a detector will be blueshifted, but that is not a relativistic effect. The relativistic effect is that, due to the slow-down caused by time dilation, the light will be slightly "redder" than what would be predicted with a Newtonian analysis.

 

[CJames]

I wasn't claiming it was an optical illusion. I'm aware that the model describes time dilation in terms of the different distances light propagates within different reference frames. I guess I wasn't too clear on this. Really my point was simply that the number of ticks somebody were to see in this scenario would be directly dependent on the nature of light, so perception of time is dependent on the nature of light.

 

[mdeng]

Einstein only said, "time is what a clock measures." He would not allow himself to be drawn into a philosophical argument. When the Michelson–Morley experiment failed to detect an ether wind, physicists set about trying to explain it. Lorentz tried to explain things his way, and came up with the length contraction equation, but he still believed there was an ether. Einstein had his own thoughts. He postulated that as long as the observer is in an inertial reference frame, when he tries to measure the speed of light he will always come up with the same number. Using this postulate and a little algebra, he discovered he could crank out Lorentz' length contraction equation, without believing in the ether. His ideas about space-time were a development of Minkowski's ideas.

This is never proven in SR, it is assumed as a postulate. However, the resulting experimental predictions are very accurate so it is considered an experimentally verified postulate.

By the way. Although the light clock is frequently used in SR thought experiments the definition of a second is not referenced to the speed of light. (Although the definition of a meter is).

I start to think that if SR is based on c as postulated by the locality principle instead of talking about light (even though it does help visualize SR's consequence), the space-time relativity would somewhat follow more naturally.

In other words, if we could prove the locality principle and derive from it the c constant (in some unit), it would then entail the whole special relativity theory and likely provide better insight too.

And perhaps, if there is another world where locality principle does not always apply (as some claims in quantum world), we may derive something else (I guess).