KJW

That's not quite true. The CMBR represents the time the universe became transparent to electromagnetic radiation. However, it is proposed that before then, there was a time when the universe became transparent to neutrinos, and therefore the cosmic neutrino background may be something before the CMBR that could in principle be studied.

We are in agreement about the need of quantum mechanics to have an ontology. The "shut up and calculate" viewpoint is wholly unsatisfactory. However, we do disagree about the ontology itself, and maybe also about the relationship between mathematics and physics. The ontology I see is something like the many-worlds interpretation. I say "something like" because I haven't quite worked out the precise details, and I feel that the usual presentation of the many-worlds interpretation is problematic, although it is not clear to me if these problems extend to the original relative state formulation by Hugh Everett. Nevertheless, I do regard the wavefunction to be not so much about a particle, but about the entire reality in which the particle exists, including the entire history and future of the reality. Then the reality that includes the [math]|\psi_1\!\!>[/math] state also includes the [math]|\phi_1\!\!>[/math] state, and the reality that includes the [math]|\psi_2\!\!>[/math] state also includes the [math]|\phi_2\!\!>[/math] state. Thus, non-locality is taken care of without invoking any interaction between the two states. Note that the no-communication theorem says that there is nothing that can be done to the [math]|\psi\!\!>[/math] state that will affect the result of a measurement of the [math]|\phi\!\!>[/math] state. That is, although the correlation between distant states is strange, it is not strange enough to require interaction between the distant states. I believe that the ontology of quantum mechanics needs to connect with the mathematics of quantum mechanics. The notion that there is an underlying physical mechanism that is not a part of the mathematics seems wrong to me. I didn't discuss the violation of Bell's inequalities because I was discussing the nature of quantum entanglement. I wasn't trying to prove that quantum physics cannot be explained classically. Bell's inequalities aren't exactly about quantum entanglement. They are limitations on the properties of classical states. Their violation in quantum entanglement experiments demonstrate that the correlations that occur between quantum entangled states cannot be explained in classical terms. But this is more about the nature of quantum states than about entanglement. There is no mention of locality within Bell's inequalities. The notion of locality is merely to close a loophole in Bell's theorem concerning the possibility of communication between entangled distant states. Thus, it seems to me that by making the distant states local via an extra dimension, you are claiming that it is necessary for the result of a measurement of one state to be communicated to the other state. The mathematics does not seem to point to this notion. The correlation between quantum entangled states is already a part of the multi-particle state and doesn't need to be reinforced by a communication of measured results between states. [If the above LaTex doesn't render, refresh the page]

MythBusters did an episode in which something like this was tested: MythBusters Episode 217: Household Disasters Premier Date: July 17, 2014 ... A dog bowl can focus the sun’s rays at a small enough point to start a fire due to it being very hot.CONFIRMED The Build Team sets up a table on a wooden deck outside on a sunny day, made to look like a picnic, and put out highly flammable objects to improve their chances. This includes dried flowers, decaying wood, and paper. They set two types of dog bowls, metal and glass, in various sizes to focus the sun’s rays. Due to high humidity and wind, they use a theatrical light to warm up the set, replicating ideal conditions of the summer. The temperature of the set was 105 °F (41 °C), with 12% humidity. After two minutes, the glass bowls started a fire on the set, confirming the myth under ideal conditions. (This segment was not shown in the U.S. broadcast.) ... There was also the 20 Fenchurch Street skyscraper in London, nicknamed "The Walkie-Talkie", which during its construction, due to its concave reflective surfaces, focused sunlight onto the street below, causing damage to parked vehicles.

"Residual Order" Equation for Tensors I couldn't think of a better name for this topic. Anyway, it is about a concept in tensor calculus similar to dimensional analysis in physics. In physics, one has the dimensions of length, time, mass, etc. In geometry, there is only length. However, there are other "weights", as well as "orders". The "residual order" equation expresses a relation between these, and indicates what constitutes a <b>properly definable quantity</b>. First, it is necessary to define some terms (most of which I coined):<br><br> For the tensor T^{i1 ... ip} _{j1 ... jq} (and other indexed quantities properly expressed as such):<br><br> Define the CONTRAVARIANT ORDER as p.<br> Define the COVARIANT ORDER as q.<br> Define the TOTAL ORDER as p+q.<br> Define the RESIDUAL ORDER as p-q.<br><br> It is the RESIDUAL ORDER that is of interest here. The residual order has an important property: it is unchanged by the contraction of any number of pairs of indices (because q is decreased by the same amount as p).<br><br><br> Every tensor possesses three weights:<br><br> (1): TENSOR WEIGHT<br><br> For tensor <b>A</b>, transforming as <b>A</b>' = <b>A</b> |<font face="Symbol">¶</font>x^j/<font face="Symbol">¶</font>x'^s|^T ...(etc) under a coordinate transformation, define the TENSOR WEIGHT as T.<br><br> (2): DIMENSION WEIGHT<br><br> For tensor <b>A</b>, transforming as <b>A</b>' = k^D <b>A</b> under the change of length units dx'ⁱ = k dxⁱ (not a coordinate transformation), where k is an arbitrary non-zero constant, define the DIMENSION WEIGHT as D. This corresponds to the length dimension in physics. However, in geometry, this is the only dimension and all other dimensions of physics can be expressed in terms of length by the application of the fundamental constants.<br><br> (3): METRIC WEIGHT<br><br> For tensor <b>A</b>, transforming as <b>A</b>' = k^M <b>A</b> under the change of scale g'^ij = k g^ij, where k is an arbitrary non-zero constant, define the METRIC WEIGHT as M. Although this is called the "metric" weight, note that the scale transformation is applied to the INVERSE of the metric tensor. This is to maintain a convention that seems to exist throughout tensor calculus.<br><br> These weights can also be defined for quantities that are not tensors.<br><br><br> STANDARD WEIGHTS are quantities that have a weight of +1 or -1 for their particular weight type, but have a weight of 0 for the other weight types.<br><br> TENSOR: The permutation symbols e^{i1 ... in} and e_{i1 ... in} (n = dimension of the space) have a TENSOR weight of +1 and -1, respectively. The DIMENSION and METRIC weights are both 0.<br><br> DIMENSION: The differential dxⁱ and the partial differentiation operator <font face="Symbol">¶/¶</font>xⁱ have a DIMENSION weight of +1 and -1, respectively. The TENSOR and METRIC weights are both 0.<br><br> METRIC: The inverse of the metric tensor g^ij and the metric tensor g_ij have a METRIC weight of +1 and -1, respectively. The TENSOR and DIMENSION weights are both 0.<br><br><br> The four orders and three weights defined above separately obey two rules:<br><br> (1): Only quantities of the same weight (or order) can be added, subtracted or equated. There exists a zero quantity for all orders and weights.<br><br> (2): For the weights (or orders) W(A) and W(B) of quantities A and B, the weight of the outer product AB, W(AB) = W(A) + W(B). However, the RESIDUAL ORDER and the TENSOR, DIMENSION and METRIC weights are unchanged by the contraction of any number of pairs of indices. Therefore, the outer product can be combined with the contraction of any number of indices without changing the value of the RESIDUAL ORDER or the TENSOR, DIMENSION and METRIC weights.<br><br><br> The Residual Order Equation:<br><br> For RESIDUAL ORDER = R, TENSOR WEIGHT = T, DIMENSION WEIGHT = D, and METRIC WEIGHT = M:<br><br> R = nT + D + 2M <br><br> (n = dimension of the space)<br><br><br> Examples:<br><br><font face="Courier"> . R . T . D . M . Quantity<br> --------------------------<br> . n . 1 . 0 . 0 . Permutation symbol e^{i1 ... in}<br> .-n .-1 . 0 . 0 . Permutation symbol e_{i1 ... in}<br> . 1 . 0 . 1 . 0 . Differential dxⁱ<br> .-1 . 0 .-1 . 0 . Partial differentiation operator <font face="Symbol">¶/¶</font>xⁱ<br> . 2 . 0 . 0 . 1 . Inverse of the metric tensor g^ij<br> .-2 . 0 . 0 .-1 . Metric tensor g_ij<br> . 0 . 0 . 0 . 0 . Kronecker Delta (identity matrix) <font face="Symbol">d</font>ⁱ_j<br> . 0 . 0 . 0 . 0 . Generalised Kronecker Delta <font face="Symbol">d</font>ⁱ¹_j1^._.^._.^._.^ip_jp<br> . 0 . 2 . 0 .-n . Determinant of metric tensor g<br> . 0 . 0 . 1 .-½ . Arc-length s<br> . 1 . 0 . 0 . ½ . Unit tangent vector (n-velocity) dxⁱ/ds<br> . 0 .-1 . n . 0 . Volume element dV<br> . 0 . 0 . n .-½n. Volume <font face="Symbol">ò</font>_R |g|^½ dV<br> .-3 . 0 .-1 .-1 . Partial derivative of metric tensor <font face="Symbol">¶</font>_ig_jk<br> .-1 . 0 .-1 . 0 . Christoffel symbol <font face="Symbol">G</font>_ij^k<br> .-2 . 0 .-2 . 0 . Riemann tensor R_ijk^l<br> .-4 . 0 .-2 .-1 . Riemann tensor R_ijkl<br> . 0 . 0 .-2 . 1 . Riemann tensor R_ij^kl<br> . 0 . 0 .-2 . 1 . Magnitude of Riemann tensor |g^ir g^js g^kt g_lu R_ijk^l R_rst^u|^½<br> .-2 . 0 .-2 . 0 . Ricci tensor R_ij<br> . 0 . 0 .-2 . 1 . Ricci tensor R_i^j<br> . 2 . 0 .-2 . 2 . Ricci tensor R^ij<br> . 0 . 0 .-2 . 1 . Ricci scalar R<br> .-2 . 0 .-2 . 0 . Einstein tensor G_ij<br> . 0 . 0 .-2 . 1 . Einstein tensor G_i^j<br> . 2 . 0 .-2 . 2 . Einstein tensor G^ij<br> .-2 . 0 .-2 . 0 . Weyl conformal tensor C_ijk^l<br> .-4 . 0 .-2 .-1 . Weyl conformal tensor C_ijkl<br> . 0 . 0 .-2 . 1 . Weyl conformal tensor C_ij^kl<br> .-3 . 0 .-3 . 0 . Covariant divergence of Weyl conformal tensor <font face="Symbol">Ñ</font>_uC_ijk^u<br> . 0 . 0 . 0 . 0 . The topological invariant <font face="Symbol">ò</font>_R R_{[i1 i2} ^{i1 i2} ... R_{in-1 in]}^{in-1 in} |g|^½ dV</font><br><br><br>

Maybe that's what's happening with Trump.

Basically, quantum entanglement occurs when a quantum state that is a superposition of basis states interacts with another state such that each of the basis states interacts differently with the other state. This can be represented mathematically (with some abuse of notation): Let: [math]|\Psi\!\!> = |\psi_1\!\!> +\ |\psi_2\!\!>[/math] When this state interacts with [math]|\Phi\!\!>[/math]: [math]|\Phi\!\!>\ ^{\underrightarrow{|\psi_1>}}\ \ |\phi_1\!\!>[/math] [math]|\Phi\!\!>\ ^{\underrightarrow{|\psi_2>}}\ \ |\phi_2\!\!>[/math] This produces the superposition of two-particle states: [math]|\phi_1\!\!>|\psi_1\!\!> +\ |\phi_2\!\!>|\psi_2\!\!>[/math] Because this superposition of two-particle states cannot be decomposed as the tensor product of two single-particle states, it is an entangled state. A measurement of [math]|\psi\!\!>[/math] is an implicit measurement of [math]|\phi\!\!>[/math] and visa-versa. And the result of such a measurement will be perfectly correlated. That is, [math]|\psi_1\!\!>[/math] will produce [math]|\phi_1\!\!>[/math] only, and [math]|\psi_2\!\!>[/math] will produce [math]|\phi_2\!\!>[/math] only. Two key aspects of the entanglement are (1): the interaction that leads to the dependence of one particle state on another particle state (the correlation), and (2): the quantum superposition of multiple-particle states. It is this second aspect that makes quantum entanglement a peculiarly quantum phenomenon. Thus, the "mechanism" of quantum entanglement should really be about the quantum superposition and not about any appearance of non-locality. [If the above LaTex doesn't render, refresh the page]

Of course you are right to mention that my proposition does not work in any frame - but i did mention explicitly that this construction requires to start from the preferred frame i.e. where the medium is at rest. Now, if we have an equation in one frame and need it in another, we can do the corresponding transformation. For the sound equation we would normally do that by Galilean trafos and hence get additional terms for the medium, right? But starting from the base frame we can now apply also a Lorentz trafo and get an equation without a medium - but in different coordinates. Before my previous post, as well as since your last post, I had spent considerable time over this issue. I must say that what you are saying here is correct. I had been misled by the known physics into believing that one required the complete wave equation in order to apply your modified Lorentz transformation. But in fact, your modified Lorentz transformation, as a coordinate transformation, can be applied to the incomplete wave equation that is valid in the particular coordinate system to which the modified Lorentz transformation is being applied. And in the new coordinate system, the incomplete wave equation is valid due to the invariance of the incomplete wave equation to the modified Lorentz transformations. But we know that for observers in frames of reference in which the medium is not at rest, the incomplete wave equation is not valid and that the observed speed of sound will depend on the speed of the medium relative to the observer. Thus, we can conclude that the new coordinates produced by the modified Lorentz transformations do not represent the space and time of any observer. The space and time of observers is governed by the speed of light in a vacuum. Also, it may be concluded that the principle of special relativity only applies to space and time and not to the coordinates produced by your modified Lorentz transformations.

Perfluorooctanesulfonic acid?

[math]\ket{\Phi}\ ^{\underrightarrow{\ket{\psi_1}}} \ket{\phi_1}[/math]

Did you read the second paragraph? "Quantum nonlocality does not allow for faster-than-light communication, and hence is compatible with special relativity and its universal speed limit of objects. Thus, quantum theory is local in the strict sense defined by special relativity and, as such, the term "quantum nonlocality" is sometimes considered a misnomer. Still, it prompts many of the foundational discussions concerning quantum theory."

Quantum teleportation uses a classical communication channel as well as a quantum channel to transfer information about the quantum state to the other location.

The press release does not mention "local" (or any word containing "local")

But Bell's inequalities do not imply non-locality in the sense of an interaction between distant locations. The no-communication theorem of quantum mechanics forbids this type of non-local interaction. In the absence of non-locality, Bell's inequalities do seem to deny counterfactual definiteness. The notion of counterfactual definiteness suggests that quantum wavefunctions represent a lack of knowledge rather than the reality itself, and therefore quantum mechanics would seem to deny counterfactual definiteness rather than deny locality.

The total force is 0 N because force is a vector and the vector sum of all the forces on the object is 0 N. By the way, have you ever seen this problem?

Do you have a proof of this? Whenever someone mentions something like this, I am reminded of the Burnside problem in mathematics. Normally expressed in terms of group theory, it can be interpreted in terms of a string of characters. The problem itself is quite general, but there is a specific case which remains an open problem: Suppose one has a string of characters from an alphabet of two characters (a binary number perhaps). Suppose also that no substring of any length repeats five or more times in a row. The question is: Is the string necessarily finite? An answer of "no" to this open problem invalidates the reasoning you applied in this thread for it would indicate that an infinite string doesn't necessarily contain all possible substrings, such as a substring that repeats five or more times in a row. I don't know the answer to this problem, but it does provide food for thought regarding the idea that an infinite space necessarily contains all possibilities.

No. I was not applying Birkhoff's theorem to energy-radiating processes. I was applying it to the case of a spherically symmetric object that expands, contracts, or arbitrarily pulsates due to its own internal processes, without absorbing or emitting energy. For any spherically symmetric spacetime such that outside of some sphere, the Ricci tensor is everywhere zero, the metric outside of this sphere will be the Schwarzschild metric of constant mass irrespective of anything that happens inside the sphere (provided spherical symmetry is maintained). The condition that the Ricci tensor is zero everywhere outside the sphere ensures that there is no addition of energy to or subtraction of energy from the inside of the sphere. That is not necessarily true. It may be that the release of gravitational binding energy as the system contracts is absorbed by a chemical reaction. And even if radiation is emitted, this emission is not generally concomitant to the release of gravitational binding energy. Thus, the decrease in total mass does not necessarily correspond to the change in gravitational binding energy. One form of radiation that is never emitted from spherically symmetric distribution of energy-momentum is gravitational radiation. I didn't make that claim with regards to the emission of radiation. In my second post, I said the opposite.

Well, it isn't. I'm not arguing that MWI must be false because it is unbelievable in this way. I am merely pointing out that most people do indeed find it unbelievable, and that is one of the main reasons that it has remained a fringe theory instead of commanding a consensus. That's an argument from incredulity. And your interpretation seems to rely on MWI being untenable, so your reliance on an argument from incredulity is especially problematic. Well, I believe in some form of MWI because it provides a genuine explanation for the intrinsic randomness of quantum mechanics. As I see it, a measurement of a quantum state, which can be regarded as a superposition of basis states corresponding to the possible values of the observable being measured, is an interaction between the quantum state and the macroscopic measuring device such that the measuring device responds differently to each of the different basis states, producing a superposition of macroscopic measuring device states that are in quantum entanglement with the superposition of basis states of the quantum state. When we observe the superposition of measuring device states, the resulting superposition of conscious states became quantum entangled with the measuring device states and hence also with the basis states of the quantum state. Each conscious state of the superposition subjectively experiences a single measuring device state of the superposition because the individual states of the macroscopic superposition are orthogonal, and orthogonal states do not exhibit interference. Note that macroscopic states are almost always orthogonal because arbitrarily chosen vectors in a high-dimensional Hilbert space are almost always orthogonal. If the problem is that there is no consensus, then that is a problem you will never solve.

Did you not see my post before the one you quoted? The post you quoted was connected to the one before it. In that post, I was saying that in general relativity, when a spherically symmetric distribution of matter expands or contracts or arbitrarily pulsates, the external gravitation does not change, implying that the total mass does not change. The second post was merely to clarify an aspect I overlooked in the first post.

I should remark that if the radius decreases, the change in gravitational binding energy would ultimately result in a corresponding change in thermal energy, which would eventually radiate away from the spherical object, resulting in a decrease in total mass corresponding to the change in gravitational binding energy. I suppose it is this change in total mass due to gravitational binding energy that the OP is referring to rather than energy-conserving transformation of gravitational binding energy to thermal or other energy during gravitational collapse.

According to general relativity, this is incorrect. Birkhoff's theorem states that any spherically symmetric solution of the vacuum field equations must be static and asymptotically flat. This means that the spacetime outside of any spherically symmetric distribution of energy-momentum must be given by the Schwarzschild metric. It may be considered the general relativistic version of the shell theorem in Newtonian gravity. The significance of Birkhoff's theorem to what you wrote is that if any spherically symmetric object expands or contracts or arbitrarily pulsates, then the external gravitation does not change. In other words, the Newtonian gravitational binding energy, which depends on the radius of the spherical source of gravitation, does not produce a change in the total mass of the spherical source of gravitation as the radius changes.

The defining feature of a lightlike trajectory in spacetime is that at all points along the trajectory, in all coordinate systems: guv dxu dxv = 0 That is, guv dxu dxv is a constant over the lightlike trajectory and invariant with respect to coordinate transformations. And because the chosen lightlike trajectory is arbitrary, guv dxu dxv is also constant over all possible lightlike trajectories. guv dxu dxv can't be non-zero because that would mean the trajectory is either timelike or spacelike, depending on whether guv dxu dxv is greater than or less than zero. Quite simply, spacetime does not admit the notion of a variable c, and this has nothing to do with how units of time and length are defined. Furthermore, for guv dxu dxv ≠ 0, the magnitude of an interval on the trajectory depends on the chosen endpoints of the interval. This is not the case for a lightlike trajectory, for which the magnitude of the interval is always zero regardless of the chosen endpoints. This makes the speed of light in a vacuum quite special compared to other speeds (even superluminal speeds). One thing you seem to be overlooking throughout this entire discussion is that one can't directly compare two arbitrarily chosen spacetime intervals. To perform an indirect comparison, one uses a physical object such as a clock or ruler to transfer the magnitude from the location of one interval to the location of the other interval. This relies on the magnitude not changing during the transfer from one location to the other. In the case of a clock or ruler being based on the laws of physics, it relies on the laws of physics not changing during the transfer from one location to the other. Thus, the first postulate of special relativity states that the laws of physics take the same form in all inertial frames of reference. (Note that in general relativity, local physics is special relativity). Now, the last statement depends on you choice of a metric. i know this is not an easy one to understand, especially given out intuition, but with math we can do a lot of trickery that defies intuition. Let's recall what Lorentz transformation originally are: coordinate transformations. so let's forget all interpretation and look at reality entirely from the perspective coordinates give us. Let's start with sound waves in a frame x at rest to the medium and pick some other frame x' which moves with a velocity v. What would happen if we apply a Lorentz coordinate trafo from x to x' but using c_s, the speed of sound, instead in the transformation? how does the sound wave equation look like in the new coordinates x'? Alternatively we can get the same answers when we start with the sound wave equation and ask ourselves under what kind of coordinate transformations this equation will remain invariant under? I think I understand what you are saying. You are saying that because the wave equation for sound is the same as the wave equation for light but with the speed of sound replacing the speed of light, the wave equation for sound will be invariant to Lorentz transformations with the speed of sound replacing the speed of light, and all of relativity will apply with the speed of sound replacing the speed of light. This would be true except that your initial premise is not true. The wave equation for sound: ∂2φ/∂x2 + ∂2φ/∂y2 + ∂2φ/∂z2 − 1/csound2 ∂2φ/∂t2 = 0 is incomplete. It is incomplete because there is no mention of the speed of the medium. Thus, the equation only applies to the frame of reference in which the medium is at rest. Therefore, the above wave equation is not invariant to Lorentz transformations with the speed of sound replacing the speed of light, and the rest of relativity doesn't apply either. Within the acoustic metric, the formulas become identical. But they are not physically identical. Consider the transverse Doppler effect. For sound, there is no transverse Doppler effect, whereas for light in a vacuum, there is a Doppler effect corresponding to time dilation. An important property of tensors is that a tensor that is zero (or non-zero) in one coordinate system is zero (or non-zero) in every coordinate system. A corollary of this is that a tensor equation that is true in one coordinate system is true in every coordinate system. Ideally, the laws of physics are tensor expressions. This makes sense because physical reality doesn't come with a coordinate system, and therefore the behaviour of physical reality is independent of any coordinate system. General relativity is explicitly about tensors. The idea of removing a background indicates the background is not a tensor and therefore goes against the spirit of relativity. As I said above, the above wave equation for sound is incomplete and valid only in the frame of reference in which the medium is at rest. This also means that the complete equation that reduced to the above equation is not a tensor equation (three-dimensional velocity is not a tensor).

This looks to me like an argument from incredulity.

From what I have read (I haven't watched any of the videos), he did identify himself, and that claims that he didn't identify himself or that he was threatening were blatant lies. It was also suggested that if they're willing to lie about events that took place in a room full of reporters, then what wouldn't they lie about?

It took me a while to figure out that all one needs to do is paste the URL of the image directly into the post. It defaults to imbedding the image but provides the option to display the link instead. One can then manipulate the size of the image. There is also a "Media Options" button at the top-right of the image.

It would appear that you believe reality has a non-trivial topology. I'm actually quite ambivalent about whether or not spacetime has a non-trivial topology. Anyway, I do consider the question of whether two different descriptions are describing the same reality to be a fundamental question. However, one shouldn't be blasé about what characterises equivalent descriptions. It is something that requires careful consideration. I do believe that reality does have more structure than what is provided by topology. Yeah, and it is the same two experiments also with the old standard, as the old one standard of length is still based on a derivative of the speed of light and therefore has no potential of deviation. This is my what bothers me. ... Your line of thought only works if the alternative standard of length used in an experiments can be considered sufficiently independent of c. I was actually addressing the concern that I was measuring the speed of light using a standard of length based on the speed of light. Anyway, there was a time when the standard of length was based on a platinum-iridium bar. How is the length of a platinum-iridium bar based on the speed of light? Actually, you did suggest that because atoms are based on electromagnetism that their size is based on the speed of light. But you didn't explain precisely how the electromagnetism of the atom leads to the size of the atom being based on the speed of light. On the other hand, given the fundamental connection between space and time that is manifested by the speed of light, it may be that a standard of length that is not based on the speed of light is impossible. That is, you may have a problem with a standard of length being based on the speed of light, but if it is impossible for a standard of length to be independent of the speed of light, then this becomes problematic to your idea that the speed of light can vary. and this idea works for any wave, not just light. the acoustic metric is a perfect example of that. it shows that we can treat sound waves identical to light in a vacuum with curvature and using that special definitions of time and space we get all the familiar framework. One can't replace the speed of light in a vacuum with the speed of sound. One can't even replace the speed of light in a vacuum with the speed of light in water. In the measurement of c based on the measurement of the speed of light in both still water and moving water, the choice of using light in water was merely to provide a speed that is fast enough for the relativistic effect to be significant. In principle, one could choose the speed of any object to apply the relativistic velocity-addition formula. Although like the speed of light in a vacuum, the speed of sound in a medium is constant with respect to the speed of the source, unlike the speed of light in a vacuum, the speed of sound in a medium is not constant with respect to the speed of the observer. The speed of sound in a medium is constant relative to the medium and therefore does not depend on the speed of the source relative to the medium. But the speed of sound relative to the observer does depend on the speed of the observer relative to the medium. The important role played by the medium with regards to sound in contrast to the absence of a medium with regards to light in a vacuum manifest in the difference in the Doppler effect formula for sound and for light in a vacuum.