# Relativity of Simultaneity and frames

• I
• Conservation
In summary: ...simultaneously measure the distance between two observers and the time it takes for light to travel between them.
Conservation
Hello everyone, sorry if this is a noob question; I'm just starting out with special relativity.

I was wondering whether relativity of simultaneity is a direct consequence of our ability to "know" being dependent on sight (light reaching a point). If, for example, we could only judge an event occurring based on smell or a rock being thrown towards us from the event point, and the clocks were synchronized accordingly for those methods, would the relativity of simultaneity still hold? Would simultaneous events at one reference still not be simultaneous in another reference frame?

Conservation said:
I was wondering whether relativity of simultaneity is a direct consequence of our ability to "know" being dependent on sight (light reaching a point).
No, it is neither a direct nor an indirect consequence. It actually is a consequence of the fact that c is invariant. The speed, c, would be invariant regardless of what mechanism of information transfer we were to use.

The glib answer is that a blind person can still build a radar set.

The deep answer is that there is an invariant speed (one that is the same measured in any inertial frame of reference) as a consequence of the rules of Minkowski geometry and you don't actually need anything to be able to travel at that speed in order to derive those rules.

A possibly more helpful answer is to note that, I would guess, you have been shown Einstein's train as a way to derive relativity. It's very tempting to view that as being all about what people see, although it isn't. The "light clock" is a better way of convincing yourself, to my mind, because it's all about measuring round trips of light pulses, rather than discussing when two remote things actually happened.

You can synchronize clocks either by light or by piece of sh,. It is important that its velocity in different directions would be the same for every observer, if you need "relativity of simultaneity".

It would be a little bit better to consider relativity of simultaneity this way:

To make proper conclusion, at what time certain event will take place in certain place (coordinate) of reference frame, you must to have a clock in that place. Procedure for every observer looks like this thought experiment. An observer in a train and observer on the platform allocate (place) clocks along platform and along the train. For example, any observer can put synchronized clocks in his reference frame every feet. Then each observer synchronizes all clocks in his own reference system by means of Einstein technique, admitting that speed of light in each direction for every inertial frame is the same. Then all clocks in his reference system show the same time, a clock on observer’s wrist and a clock a million miles away from the observer. If event happens in that place one million miles away, now he knows time of event in his frame. Since frames are in relative motion, that leads to so-called relativity of simultaneity. Simultaneous evens in reference frame K will be not simultaneous in reference frame K’. Adjacent clocks of different frames will show different time. This way of thinking puts thoughts in order.

It also quite important to note, that in this case observer in special relativity is not quite a single person, who turns his head and looks by eyes. It is often said, that a team of observers does measurements. Every observer possesses clock and takes readings of other clock (from another reference frame) in immediate vicinity (straight in front of him).

https://en.wikipedia.org/wiki/Observer_(special_relativity)

Very good article with very clear definitions:

https://arxiv.org/ftp/physics/papers/0512/0512013.pdf

Important note on time dilation: single clock moves in a reference frame, which is “filled” with synchronized clocks. Single clock dilates, not vice versa.

Please look at “reference frames”, “time dilation”

http://isites.harvard.edu/fs/docs/icb.topic455971.files/l09.pdf

It should be noted, that every observer uses his own reference frame while measures moving clock rate and length of a moving in his reference frame measuring rod. We call this frame "rest frame", since an observer is "at rest" in this frame and other material bodies and clocks move in it.

John is at rest first and Bob moves in his frame. John measures that Bob contracts and dilates.

Then Bob is at rest and John moves in his frame. Bob measures that John contracts and dilates.

Bob shorter than John, John shorter than Bob. This is Special Relativity.

Special relativity claims, that state of proper motion is no different from the state of proper rest. That's why every observer may consider himself being "at rest" and to conduct measurements in his own rest frame.

However, there are other ways to observe relativistic effects without introducing Einsteins measuring technique by means of synchronized clocks (which ADMITS that speed of light in different direction is the same for ever observer. Good to know that nobody has ever measured one way speed of light). For example, you can simply look at a relatively moving lamp. If you look at the lamp at right angle to direction of it’s motion, you will see, that lamp changes color, because for you it oscillates slower due to time dilation. Blue lamp will turn green and green lamp will turn red. This is so - called Transverse Doppler Effect, which has no analogue in classical mechanics.

You can also measure length contraction by photo camera. You can make a picture of moving object and to look how it appears on it. The moving object (measuring rod, or better a moving square) must attach lamps at the ends and to release a flash simultaneously in his reference frame. For example, a square can put a lamp at each corner ABCD. These lamps will flash simultaneously, if the flashes are synchronized by means of a beam from the center.

I mean center of the square is in the origin and the square is in xz plane.

By magnitude of distortions you can evaluate relativistic contraction. Side BC will be gamma times shorter than AB.

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FactChecker
@Ibix , or gamma times longer?

Conservation said:
Hello everyone, sorry if this is a noob question; I'm just starting out with special relativity.

I was wondering whether relativity of simultaneity is a direct consequence of our ability to "know" being dependent on sight (light reaching a point). If, for example, we could only judge an event occurring based on smell or a rock being thrown towards us from the event point, and the clocks were synchronized accordingly for those methods, would the relativity of simultaneity still hold? Would simultaneous events at one reference still not be simultaneous in another reference frame?

You'd get basically the same results according to relativity if you threw rocks - or more reasonably electrons - or protons - or ions - or atoms - or molecules. "Smell" would require throwing molecules (that's how smell works), so it's not any different for this purpose than throwing rocks, for a suitably general definition of "rock".

If you threw "rocks" (by which I mean any of the things I previously listed, not specifically just rocks) instead of light, you'd have the additional complicating factor that you'd expect the time delays that you'd need to account for, the time delays for the rock to reach it's destination to possibly depend on how hard you threw the "rock". So it'd be more work to set up and analyze. Also, the slower you throw your "rock", the more potential for experimental error there is due to the travel times being longer. Light is the fastest possible thing you can throw, and you don't need to worry about "how hard" you throw it, because it always moves at the same speed, so it's ideal. But it's not fundamentally necessary to use it - just convenient and practical.

You'd also find that if you threw "rocks" sufficiently hard, they'd reach a limiting velocity, and that limiting velocity would be "c", the speed of light. This is not particularly intuitive, but it's what relativity predicts, and is consistent with experimental results based on throwing electrons. See for instance the video "The Ultimate Speed", , or the original paper by Bertozzi in the literature. Basically, in the experiment, electrons are thrown as hard as was available at the time the experiment was done, and the delays were measured. The results (time delay vs how hard) were graphed, and are consistent with relativity, and inconsistent with Newtonian physics.

Battlemage!
pervect said:
"Smell" would require throwing molecules (that's how smell works), so it's not any different for this purpose than throwing rocks, for a suitably general definition of "rock".
Then I'll wear deodorant and a catcher's mask if we ever meet up, pervect...

Battlemage!
Conservation said:
I was wondering whether relativity of simultaneity is a direct consequence of our ability to "know" being dependent on sight (light reaching a point).

If I understand you correctly, you are referring to what are called look-back effects or how the finite speed of light affects how we see things. These are purely classical effects and have nothing to do with relativity.

pixel said:
If I understand you correctly, you are referring to what are called look-back effects or how the finite speed of light affects how we see things. These are purely classical effects and have nothing to do with relativity.

I believe there are some slight differences between classical and relativistic "look-back effects". By the way, this is a term I haven't seen before, but it seems apt. Anyway, if we consider for instance the aberration of light, which is the apparent change in the direction of light when seen from a moving source, there are different formula given in Wiki (LINK) for classical and relativistic aberration of light.

One common issue is that people don't want to deal with "look-back" effects. Which is understandable, however if one wants to compare experiment to theory, one needs to account for this class of effect to do a proper comparison. And there are differences in the results when one takes into account the relativity of simultaneity, so it must be included.

The relativity of simultaneity is just one part of special relativity, but it's an important part. The theory won't work without it. It's also a part of the theory that people usually have trouble with, they seek for ways to avoid it. But it's part of special relativity, SR just won't work without the relativity of simultaneity.

pervect said:
I believe there are some slight differences between classical and relativistic "look-back effects". By the way, this is a term I haven't seen before, but it seems apt. Anyway, if we consider for instance the aberration of light, which is the apparent change in the direction of light when seen from a moving source, there are different formula given in Wiki (LINK) for classical and relativistic aberration of light.

Walter Scheider uses the term "look-back time" in his book, Maxwell's Conundrum. I don't recall seeing it anywhere else.

My point was just that relativity deals with events as determined in reference frames (which assume a distribution of clocks and observers at rest with respect to each other) and not how a single observer might witness an event as a result of the finite speed of the light reaching his eyes.

pixel said:
My point was just that relativity deals with events as determined in reference frames (which assume a distribution of clocks and observers at rest with respect to each other) and not how a single observer might witness an event as a result of the finite speed of the light reaching his eyes.

This is much too limited a view of what relativity "deals with". Relativity certainly includes effects arising from the finite speed of light. Nor are reference frames required to either formulate or use relativity; they are conveniences, not necessities.

pixel said:
These are purely classical effects and have nothing to do with relativity.

Classical (pre-relativity) physics, as far as relativity is concerned, is not an alternate theory for explaining some things while relativity deals with the rest. Classical physics is just an approximation to relativity that works when everything is moving slowly compared to the speed of light (and gravitational fields are weak, if we are talking about general relativity instead of special). There is no such thing as a "purely classical" effect that has nothing to do with relativity. There are just effects that occur in the classical approximation and other effects that don't (or more precisely are too small to matter in that approximation).

pervect said:
You'd get basically the same results according to relativity if you threw rocks - or more reasonably electrons - or protons - or ions - or atoms - or molecules. "Smell" would require throwing molecules (that's how smell works), so it's not any different for this purpose than throwing rocks, for a suitably general definition of "rock".

If you threw "rocks" (by which I mean any of the things I previously listed, not specifically just rocks) instead of light, you'd have the additional complicating factor that you'd expect the time delays that you'd need to account for, the time delays for the rock to reach it's destination to possibly depend on how hard you threw the "rock". So it'd be more work to set up and analyze. Also, the slower you throw your "rock", the more potential for experimental error there is due to the travel times being longer. Light is the fastest possible thing you can throw, and you don't need to worry about "how hard" you throw it, because it always moves at the same speed, so it's ideal. But it's not fundamentally necessary to use it - just convenient and practical.

You'd also find that if you threw "rocks" sufficiently hard, they'd reach a limiting velocity, and that limiting velocity would be "c", the speed of light. This is not particularly intuitive, but it's what relativity predicts, and is consistent with experimental results based on throwing electrons. See for instance the video "The Ultimate Speed", , or the original paper by Bertozzi in the literature. Basically, in the experiment, electrons are thrown as hard as was available at the time the experiment was done, and the delays were measured. The results (time delay vs how hard) were graphed, and are consistent with relativity, and inconsistent with Newtonian physics.

Thank you for that video. Very informative and totally cool how they use what looks like the same type of oscilloscope I used in Intro Physics.

It would be hard for a crank to argue against what's in that video!

PeterDonis said:
This is much too limited a view of what relativity "deals with". Relativity certainly includes effects arising from the finite speed of light. Nor are reference frames required to either formulate or use relativity; they are conveniences, not necessities.

OP was asking whether relativity of simultaneity was due to how we see things. I was merely trying to dissuade him from that notion with an example, not trying to summarize all of relativity in a single sentence.

PeterDonis said:
Classical (pre-relativity) physics, as far as relativity is concerned, is not an alternate theory for explaining some things while relativity deals with the rest. Classical physics is just an approximation to relativity that works when everything is moving slowly compared to the speed of light (and gravitational fields are weak, if we are talking about general relativity instead of special). There is no such thing as a "purely classical" effect that has nothing to do with relativity. There are just effects that occur in the classical approximation and other effects that don't (or more precisely are too small to matter in that approximation).

I think it is generally understood what is meant by a "purely classical" effect.

Battlemage! said:
It would be hard for a crank to argue against what's in that video!
It's a total waste of time to worry about what cranks can or can't argue against since they can, and will, argue with ANYTHING. If all else fails, they can just say the whole thing is a fake someone made up to dispute the truth as they know it to be.[/QUOTE]

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morrobay
Thank you for your replies everyone; I think, as pixel pointed out, I was thrown off by the notion that the effect would be dependent on the observer observing a phenomenon with his eyes, which would require light to reach. The example I was thinking of was indeed the common example of the flashing train. Pervect's reply of limiting velocities seems to have cleared that up for high speeds.

I guess my confusion mainly stems from what some of the posters above are alluding: the threshold at which classical physics breaks down and special relativity kicks in, and vice versa. It's clear, at least mathematically, that relativity of simultaneity must hold for invariance of speed of light. It is also clear that if a rock launcher (sorry for using rock again, I just like that example) slowly launches two rocks in different directions on a slowly moving train, both the observer on and off the train will see the rocks hit the wall at the same time since Galilean transformation of velocities will hold for the rocks without experiencing relativistic effects.

Conservation said:
I guess my confusion mainly stems from what some of the posters above are alluding: the threshold at which classical physics breaks down and special relativity kicks in, and vice versa.
Just to be sure you are clear, there IS no such place except inasmuch as you are specifying some particular degree of accuracy in the answer. Classical is just a limiting subset of SR for slow speeds so the more accuracy you want, the slower the speed at which classical mechanics will give you an acceptable answer.

Conservation said:
I guess my confusion mainly stems from what some of the posters above are alluding: the threshold at which classical physics breaks down and special relativity kicks in, and vice versa.
There's no threshold as such. The Galilean transforms are a low speed approximation to the Lorentz transforms. They're never strictly correct, but they are good enough for every day, and the maths is a lot simpler.

For example, the twin paradox applies when you walk to the office printer and back. If it's fifteen meters to the printer and you stride along at 3m/s then your wristwatch will show approximately 5×10-16s less have elapsed than your desktop clock.

And if we are sitting next to each other there is around ±3ns leeway in what someone would call "the same time" for us due to the relativity of simultaneity.

Even us physics nerds don't usually worry about a lack of precision that small. But you might need to for a really high precision measurement of something.

## 1. What is the concept of relativity of simultaneity?

The relativity of simultaneity is a concept in special relativity that states that the concept of "simultaneity" is relative to the observer's frame of reference. This means that events that are perceived as happening simultaneously by one observer may not be perceived as simultaneous by another observer in a different frame of reference.

## 2. How does the relativity of simultaneity relate to the speed of light?

The relativity of simultaneity is closely related to the speed of light, as described by Einstein's theory of special relativity. According to this theory, the speed of light is constant and the same for all observers, regardless of their frame of reference. This means that the perception of simultaneity is affected by the relative velocity between the observer and the events being observed.

## 3. What is an inertial frame of reference?

An inertial frame of reference is a frame in which Newton's first law of motion holds true. This means that an object in motion will remain in motion at a constant speed in a straight line unless acted upon by an external force. In special relativity, an inertial frame of reference is a non-accelerating frame, meaning that it is either at rest or moving at a constant velocity.

## 4. How does the relativity of simultaneity impact our understanding of time?

The relativity of simultaneity has significant implications for our understanding of time. It means that time is not absolute and can be perceived differently by different observers depending on their relative velocity. This is known as time dilation and is a fundamental aspect of special relativity.

## 5. Can the relativity of simultaneity be experimentally proven?

Yes, the relativity of simultaneity has been experimentally proven through various experiments, such as the Michelson-Morley experiment and the Hafele-Keating experiment. These experiments have demonstrated that the perception of simultaneity is relative to the observer's frame of reference and is influenced by the speed of light.

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