I Relativity and speed of light basics

[Orodruin]

the basic principal of SR is that the speed of light is intrinsic. All observes measure the same speed of light. Time dilation and length contraction are the way this happens.

I am fully aware how SR works, I teach relativity at advanced university level. Time dilation and length contraction are results of this, not the other way around, and you really cannot understand them properly unless you also account for relativity of simultaneity, which most laymen seem to ignore.

Observed and measure are just that.

This is your own definition. You really should avoid making your own definitions and trying to impose them on the standard nomenclature.

The photon isn’t going to tell you all the distortions that it underwent on its way from its source to your instrument.

Again, stop talking about photons. It is a common problem that people talk about photons when what they really should be talking about is light pulses. Things such as frequencies are not inherent to a light pulse, they are just components of a null 4-vector (the 4-frequency) in a particular frame. Such frames are typically what is connected to an "observer" in the sense that if someone measured the frequency using that frame they would get a particular result. However, you cannot say that a light signal has a particular frequency without implicitly referring to a frame. It would be like saying that a mountain had a slope to your right without specifying how you are turned.

SR is only going to tell you what the end result is, the measured quantity.

As I have already said, this is the only thing that is physically relevant. Anything else is just philosophy and does not belong in this discussion.

 

[Dragon27]

@Justin Hunt

And what SR tells us? We can have a giant, long spaceship, whose proper length we know (and can easily measure, while it still stands). We can then have it move relatively to us with an ultrarelativistic speed (by either accelerating it, or accelerating ourselves). We can measure the speed of it by measuring the time it takes for the bow of the ship to go from one milestone to the other (the distance between which we know). We can also measure the time it takes for the ship (as an object with length) to go through one milestone (from the bow to the stern), and (knowing its speed) to calculate its length. And SR tells us that we would get the length that its completely different from the proper one. The results of the measurements would disagree with our normal "Newtonian" intuition. Doesn't really look like an optical illusion to me.​

 

[stevendaryl]

Another example is that if we observe a spacecraft moving at realistic velocities compared to us, then it appear contracted along it length.

It's a coordinate effect, which is something more real than an illusion, but less real than a coordinate-independent effect.

If a 100 meter spaceship is length-contracted so that it is only 1 meter long, then it is literally true that at the same time that one end of the spaceship is at one location, the other end is 1 meter away. That's not an optical illusion. However, the notions of "at the same time" and "the distance between two points" are coordinate-dependent (or frame-dependent, if you prefer), so it's slightly less real than if the spaceship is crushed to only be 1 meter long.

 

[Orodruin]

It's a coordinate effect, which is something more real than an illusion, but less real than a coordinate-independent effect.

If a 100 meter spaceship is length-contracted so that it is only 1 meter long, then it is literally true that at the same time that one end of the spaceship is at one location, the other end is 1 meter away. That's not an optical illusion. However, the notions of "at the same time" and "the distance between two points" are coordinate-dependent (or frame-dependent, if you prefer), so it's slightly less real than if the spaceship is crushed to only be 1 meter long.

To illustrate this further, look at the corresponding problem in Euclidean geometry. Let us take a band $0 < x < 1$ in $\mathbb R^2$ and you ask what is the "width" of this band. You might instinctively say "one" since this is the range of the $x$ coordinate. However, if you instead introduce a coordinate system $S'$ that is turned 45 degrees relative to the original one and define "width" in the same way, i.e., the range of $x'$ values for a given $y'$ value, then you will suddenly find that the "width" in this coordinate system is $\sqrt{2}$. Did the band change just because you changed coordinates? Obviously not. The only thing that changed was what you mean by "width". This is an exact analogy to length contraction in SR. The object that you are describing in no way changes, what changes is the meaning of "length" as it is typically defined as the distance between to points at a fixed time and different inertial frames have different definitions of what it means for two events to be simultaneous.

 

[Justin Hunt]

I find length contraction very interesting and have pondered over any mechanism that could be causing it. I would imagine it has something to do with the fact that your velocity won’t change where your height and width break a plane, but it will determine how long it takes your length to pass through said plane. This somehow translates objects going near light speed into pancake type objects.

@Orodruin I understand photons are electromagnetic waves that have properties that can be defined from quantum physics, but it does have information based on what source it came from and the path it took. There is no universal observer to set a base value for properties such as frequency, but we could define an observer such that the relative velocities between the observer and source object is zero, the difference in gravitational potentials is zero etc. so that the observer does not impose any additional distortions to the object. Every object would have a different base observer in this case.

 

[Orodruin]

I find length contraction very interesting and have pondered over any mechanism that could be causing it.

There is no "mechanism" and therefore no "cause". It is just a question of what different observers mean when they say "length".

I understand photons are electromagnetic waves that have properties that can be defined from quantum physics,

This is a contradiction in terms. Electromagnetic waves are a classical phenomenon and photons are about as far into quantum field theory as you can go before you start dealing with non-Abelian gauge theories. In the quantum picture, classical electromagnetic fields are most accurately described in terms of the expectation values of coherent states, which are states that are not eigenstates of the photon number operator. As I said, you really do not want this type of complications when your aim is to discuss relativity.

There is no universal observer to set a base value for properties such as frequency, but we could define an observer such that the relative velocities between the observer and source object is zero, the difference in gravitational potentials is zero etc. so that the observer does not impose any additional distortions to the object. Every object would have a different base observer in this case.

Why would you do this? It is completely unnecessary and just a complication that requires you to know the state of motion of the source (at the time of emission as well! Generally the state of motion of the source can change after emission without changing the light signal itself). It is much more convenient to just talk about a light wave with some given 4-frequency, which is a 4-vector that together with the observer 4-velocity will completely determine the observed frequency.

I would also suggest that you leave GR (i.e., gravitation) out of it until you completely understand the SR case as it will introduce a heap of new complications that will render your construction not only unnecessary but also ill-defined in spacetimes that are not stationary.

 

[Herman Trivilino]

I am sorry if I wasn’t clear, but my issue is that the universe has to exist whether it is being observed or not.

Oh, yeah. I definitely missed that!

Whether the universe exists, under any circumstances, is a philosophical question. Note that the same can be said about the existence of anything.

To put this another way, the physics is the same whether or not you believe things exist when you're not observing them.

My thinking is that SR is more of an optical illusion rather than actual changes to the universe around you.

If you can't even think of a possible way to distinguish between those two things then the physics is the same for each of them, too.

 

[Sorcerer]

I am sorry if I wasn’t clear, but my issue is that the universe has to exist whether it is being observed or not. Unless we are living in a simulation and things only exist when we observe them... anyways, photons have to propagate through the universe some how. They travel at the speed of light after all and follow straight paths, which can be bent by gravitational forces etc. but, at any given time a particular photon has to be somewhere in the universe at a given time, unless it can be in multiple locations at the same time.

Now, if oberservers are moving at realistic velocities relative to each other they will both measure the same speed of light due to the warping of space and time predicted by SR. My thinking is that SR is more of an optical illusion rather than actual changes to the universe around you. The photon of light doesn’t care how you move about the universe, it will follow its set path regardless. However, your relative velocities will change how you perceive said photon. It is you that is changing, not the photon.

Another example is that if we observe a spacecraft moving at realistic velocities compared to us, then it appear contracted along it length. However, that spaceship sees the universe as contracted along its length including us. Obviously, we can’t both be length contracted at the same time. Which makes me think it is more of an illusion rather than a physical change.

(bold emphasis in the above quote is mine)

I have to question this notion (perhaps someone more knowledgeable can verify or refute what I say here):

If SR is an optical illusion, then things derived from it must be as well. For example, rest energy, E = mc² (something that is the same in ALL inertial reference frames). But IS it an optical illusion? When energy is converted into mass or vice versa, is that an optical illusion? Is nuclear power an optical illusion? To elaborate, in a nuclear reaction, Δm = ΔE/c². That result, which is very physically real and very measurable, is derivable from the postulates of special relativity. So how can it be merely an optical illusion?

Source on that relation above: https://chem.libretexts.org/LibreTexts/University_of_Missouri/MU:__1330H_(Keller)/21:_Nuclear_Chemistry/21.6:_Energy_Changes_in_Nuclear_Reactions

There are other things derived from special relativity that are NOT dependent upon your frame of reference (that is, that are the same for all inertial frames), such as the magnitude of the spacetime interval, proper time, and other things. These things all come from the postulates of relativity, but are universal for all inertial reference frames, so how can SR just be a collection of optical illusions?

Maybe the only illusions are the ones caused by our biases about how the universe works, which are the result of our inexperience with speeds near that of light?

 

[pervect]

the basic principal of SR is that the speed of light is intrinsic.

I'm not sure what you mean by this.

All observes measure the same speed of light. Time dilation and length contraction are the way this happens.

You omitted the relativity of simultaneity, which is also important. It could be a typo, but from the rest of your statements I believe it is an important omission in your thinking about the subject, an omission which indicates a systematic error in your understanding.

If there was no time dilation nor length contraction, then the observes would not be measuring the same speed of light. Observed and measure are just that. You only get the end result. The photon isn’t going to tell you all the distortions that it underwent on its way from its source to your instrument. SR is only going to tell you what the end result is, the measured quantity.

Except for your omission of the important principle of the relativity of simultaneity, I don't have any serious argument with what you are saying, though I'd also point out that Orodruin knows all this already.

However, the "relativity of simultaneity" doesn't seem to fit into your mental "distortion" model very well, and it's an important effect that you seem to be unaware of. Length contraction and time dilation alone are not sufficient to explain special relativity.

If we consider the Lorentz transform in units where c=1

$$x' = \gamma(x - \beta t) \quad t' = \gamma(t - \beta x)$$

See for instance https://en.wikipedia.org/wiki/Lorentz_transformation, and note that I've set c=1 for ease of exposition. (This can be done easily by using the right units - time in seconds, distance in light seconds, for instance).

When we focus on the second expression, we see that t' depends on both t and x. "Time dilation" explains the gamma factor in the dependence of t' on t, but it does not explain how or why t' depends on x. Length contraction also does not explain why t' depends on x. The thing that explains this mathematical dependence of t' on x is the relativity of simultaneity, and important part of special relativity that should not be ignored.

 

[Sorcerer]

I'm not sure what you mean by this.You omitted the relativity of simultaneity, which is also important. It could be a typo, but from the rest of your statements I believe it is an important omission in your thinking about the subject, an omission which indicates a systematic error in your understanding.
Except for your omission of the important principle of the relativity of simultaneity, I don't have any serious argument with what you are saying, though I'd also point out that Orodruin knows all this already.

However, the "relativity of simultaneity" doesn't seem to fit into your mental "distortion" model very well, and it's an important effect that you seem to be unaware of. Length contraction and time dilation alone are not sufficient to explain special relativity.

If we consider the Lorentz transform in units where c=1

$$x' = \gamma(x - \beta t) \quad t' = \gamma(t - \beta x)$$

See for instance https://en.wikipedia.org/wiki/Lorentz_transformation, and note that I've set c=1 for ease of exposition. (This can be done easily by using the right units - time in seconds, distance in light seconds, for instance).

When we focus on the second expression, we see that t' depends on both t and x. "Time dilation" explains the gamma factor in the dependence of t' on t, but it does not explain how or why t' depends on x. Length contraction also does not explain why t' depends on x. The thing that explains this mathematical dependence of t' on x is the relativity of simultaneity, and important part of special relativity that should not be ignored.

Bold is my emphasis.

Regarding this, how accurate is the following: the Lorentz transformations imply a mixing of time and space coordinates when a coordinate transformation occurs, and this is a direct result of (even a mathematical expression of) the relativity of simultaneity.

The reason I am thinking this is because it seems to me that the logical conclusion that must be drawn from these coordinate mixes is that simultaneous events in one frame cannot be simultaneous in all frames, and it also feels like an if and only if relation: that is, it also must be true that if simultaneity is relative, then any distance or time transformation must including the mixing of coordinates (by that I mean that transforming from S to S' must be going from the function S(x) to S'(x',t') and S' to S must be S'(x') to S(x, t), and the same with time transformations [I am not sure if that is legitimate notation, but I think what I'm trying to say is clear]).

Does any of that make sense and is any of it true?

Thanks!