Tag: relativity

Simultaneity and Synchronization

Identical clocks in relative motion can only be synchronized from the point of view of an observer relative to whom they both have the same speed. To anyone else they seem to be progressing at different rates and so are always unsynchronized and there’s no “becoming” about it. There is a sense in which the relativity of simultaneity forces the clocks to be unsynchronized, but it’s generally easier to understand the other way around so I’ll look at that first.

Imagine that, when you pass by me at 86% of the speed of light, we set our clocks to both read, say, t=0. Then they will both read the same time at that event but will not be synchronized because each will see the other as running at just half speed.

and that I also use light signals to set a clock that is fixed in my frame one light year away (in the direction towards which you are headed) to also read t=0 at what seems to me to be the same time.

Then when you reach that clock it will read t=1/.86 years but your own clock will read just 0.5/.86 years (so your clock and my remote clock are not synchronized). I will attribute that difference to your clock running slow but from your point of view the time on your clock is correct because the distance which I saw as 1 light year appears to you to be only half of that.

But from your point of view it has seemed that my clocks were running slow. So according to you, the clock you see as reading 1/.86 years must have started at a time 2/.86 years ago which is long before the time when we passed one another. Or in other words the clock-setting event I thought was simultaneous with our meeting was not simultaneous according to you.

Now what I have shown here is just that relativity of simultaneity is a mathematical consequence of the symmetric nature of the asynchronization of the clocks. But despite the lack of “becoming” there is also a logical connection the other way.

Imagine that I send a message to reach you when I think you are 1 year away from reaching me (ie at a distance of 1/.86 light years when travelling at 0.86c) and ask you to set your clock at t=-1 at that time and that I set my own clock at t=-1 at the moment I think that message reaches you. But relativity of simultaneity says that you will think I made a mistake and that those two clock settings did not happen at the same time. You will actually think that the time when I asked you to set your clock was after I had set my own and this will cause you to expect that when you reach me my own clock would have got to t=1 if running at the same speed as yours but yours will just be at t=-0.5. And since my clock will actually be reading t=0 at our meeting this will lead you to conclude that it must be running slowly (and so that they cannot be synchronized).

Source: (1001) Alan Cooper’s answer to The simultaneity of relativity tells us that inertial observers in relative motion disagree on whether 2 spatially separated events are simultaneous, but how does this lead to the observers’ clocks becoming unsynchronised? – Quora

Black Hole Singularities

A Quoran asks: Do black holes have a singularity? (A point inside the event horizon which is infinitely dense)?
YES, black holes are theoretical objects in the theory of General Relativity which are usually associated with singularities of space-time. But NO such a singularity is NOT “a point inside the event horizon”. As a point in space-time the black hole’s singularity is actually an event rather than a particular point or location in space; and in fact for every point inside the event horizon, the singularity event is in the future of any particle that is ever at that point. In terms of the way it looks to an observer inside the event horizon, there is no longer any sense of any “centre” but oneself, and the theoretically predicted experience is not of falling inwards but rather of getting crushed by the collapse of everything around you. ….or something like that!

Source: (1001) Alan Cooper’s answer to Do black holes have a singularity? (A point inside the event horizon which is infinitely dense)? – Quora

Length Contraction Inherent in Maxwell Equations?

There are two senses in which length contraction is “inherent” in the Maxwell/Heaviside equations.

One sense is that in some cases length contraction follows from Maxwell’s equations. FitzGerald and Lorentz showed that if the structure of matter is determined by electromagnetic forces then the equilibrium spacing of stationary particles due to purely electrostatic forces would become contracted when they are in motion due to the presence of additional magnetic forces. [And one effect of this contraction, together with a related slowing and desynchronization of clocks, would be that moving observers (using their own contracted measuring rods and slowed clocks) would not notice any effect of their own motion on the apparent speed of light (or in fact on any electromagnetic phenomena).]

Another sense is that length contraction is necessary to preserve the form of Maxwell’s equations. Poincare had already noted that if the coordinates used by a moving observer were related to those of one who is stationary by a standard Galilean transformation (ie by just a progressive shift of position with no change of length and time scales) and if Maxwell’s equations applied to (say) the stationary one then they would have to be modified in order to make correct predictions for the other. And he showed that the only kinds of coordinate transformation that leave the form of Maxwell’s equations unchanged are those involving length contraction and time dilation.

[Einstein then noted that if all the laws of physics, written in terms of the natural coordinates of an observer, have a form that is independent of the state of motion of the observer, then there is in fact no way to tell which of two relatively moving observers is “truly” stationary and whose clocks are “truly” synchronized. He therefore sought to express all the laws of mechanics (eventually also including gravity) in a form which used only the actually measured coordinates of each observer rather than those of some assumed fixed “rest”(or “aether”) frame (which would have been more complicated to do if possible, but was not actually possible to do properly because no observers could actually tell whether or not they were actually in motion).]

Source: (1001) Alan Cooper’s answer to Is length contraction inherent in the Maxwell/Heaviside equations? They do have some asymmetry. I remember reading something to this effect but can’t find it and could be wrong. – Quora

Less Time for Same Distance? 

For the traveller it’s not the same distance; due to length contraction it’s a smaller distance, and so takes less time. For the observer who sees the distance as a full light year it appears to take more than a year, but the traveller’s clocks appear slowed down and so will advance by less than that. (The time experienced by the traveller will still be more than a year unless the travel speed  exceeds , ie just over 70% of the speed of light.)

Source: (1001) Alan Cooper’s answer to It takes light a year to travel a light year, but why would it take a person less time to travel the same distance due to time dilation? – Quora

Timelike vs Spacelike

If two distinct events are such that there is any inertial frame in which they have zero spatial distance between them, then there is no frame in which they are simultaneous and so they are said to be “timelike separated”. This is because the frame in which they have zero spatial separation corresponds to an observer who sees them both happening at the same place one after the other; and for any other inertial observer, the time between them is also nonzero (since for any v<c the Lorentz contraction factor is never zero).

On the other hand, any two events which are seen as simultaneous by some inertial observer (which is different from being seen simultaneously by that observer!) are said to be “spacelike separated”. But the appearance of simultaneity is relative to the observer and only happens in one particular frame. Other inertial observers won’t see the events as simultaneous but all will agree that it would take faster than light travel to see them both at the same place – eg to actually be present at both of them.

Source: (1001) Alan Cooper’s answer to Is there relativity in simultaneity for events that have distance between them from the prespective of one frame but don’t have distance between them from the prespective of another? – Quora

Bergson vs Einstein

After reading this article twice, and yet again the paragraph where the author purports to show that “it’s wrong to think that Bergson’s idea of duration can be assimilated into the idea of psychological time”,

I am still unable to find any explanation of the difference between our internally experienced psychological time (which, by the way can not necessarily always be “aligned with external clock time”) and “the first-person experience of (Bergson’s unmeasurable) duration” (which they appear to identify as the “lived time” in terms of which “An hour in the dentist’s chair is very different from an hour over a glass of wine with friends”).

On the other hand Steven Savitt’s “solution” does not address the subjective nature of duration and appears to just identify it with the non-subjective proper time associated with a possible observer’s world line – which seems to be just giving up on the idea of any special “philosophical” time as this has always been the only kind of time that is ever discussed in relativistic physics.

Source: Who really won when Bergson and Einstein debated time? | Aeon Essays

Relativistic Mass

A Quora question asks: What is the equation that states that an object’s observed mass increases with its velocity?

It depends on what you mean by “an object’s observed mass”.

Nowadays the term “mass” is used exclusively for what used to be called the “rest mass” and is a property of the object alone that is independent of the relative velocity of the observer. So no physicist working today would say that “an object’s observed mass increases with its velocity”.

But there was a time in the past when some physicists used the term “mass” (usually, but not always, qualified with the adjective “inertial” or “relativistic”) to identify the multiplier needed to make a relativistically correct equation having the same form as Newton’s third law $#F=ma#$ (albeit only for the special case where the force and acceleration are parallel to the direction of relative motion between object and observer). So the equation you may be thinking of is $#m_{rel}=\frac{m_0}{\sqrt{1-v^2/c^2}}#$, but it is not a statement about what we now mean by “an object’s mass”. (And even adding the adjective “observed” or “apparent” doesn’t change that, as our observation of the “rest” mass is pretty much just as direct as that of the old “inertial” version.)

Despite many strident claims in other answers that it was “incorrect”, the alternative choice of using the word “mass” for $#m_{rel}#$ was in fact perfectly valid if applied correctly. It just wasn’t very useful because the resulting number $#m_{rel}#$ is not a property just of the object itself but depends also on the observer and is different (with a slightly more complicated formula) for accelerations and forces in directions other than that of the relative motion.

Source: (1000) Alan Cooper’s answer to What is the equation that states that an object’s observed mass increases with its velocity? – Quora

Explaining Relativity Without Equations

Can you explain time dilation and space contraction in relativity without using complex mathematical equations?

Yes. Any decent introductory text on relativity does this – but probably just in one or two sentences before going on to derive the actual formula (for which the apparent level of complexity of the resulting equations may depend on the reader’s experience).
The basic idea is that if two identical side-by-side trains are passing by one another and a light signal is sent when the ends from which it is sent are together, then if the trains are in relative motion the signal will reach the far end of one before the other. So if observers on both trains measure the same speed of light then their units of length and/or time must be different. Working out exactly how the coordinates used by each observer are related to those of the other does involve the use of mathematical formulas and equations, but they are well within the scope of high school algebra so whether or not you call them “complex” is a matter of perspective.

Source: (1000) Alan Cooper’s answer to Can you explain time dilation and space contraction in relativity without using complex mathematical equations? – Quora

Time Contraction

Special Relativity tells us that two inertial observers in relative motion each perceive the other to be ageing more slowly – ie each infers that the tick intervals of the moving clock appear to be dilated. But can time contract as well as dilate?

Yes, but with the proviso that the dilation or contraction is just a description of how the progress of one clock appears relative to another and that two observers will not necessarily agree on which events in their lives are simultaneous – and so can only compare average (rather than instantaneous) clock rates using the total time intervals on their clocks between events where they are together.

Two observers who separate and reunite will agree that the total time experienced by the one that felt more forces of acceleration (or of resistance to gravity if spending time near a massive object) will be less than that experienced by the other. This means that from the point of view of the one who was more accelerated (or spent more time at the bottom of a potential well) the clock of the other appears on average to have been speeded up (ie tick intervals appear contracted), while the one who remains unaccelerated interprets this as meaning that that the other’s clock tic intervals were, on average, dilated.

Source: (1000) Alan Cooper’s answer to Can time contract, as opposed to dilation? – Quora

Acceleration effect on light speed

The idea that the experience of an accelerated observer might be approximated by considering its worldline as comprising many small inertial pieces is a good one. And during each inertial step the speed of light seems to be constant everywhere. But at the velocity boosts or “frame jumps” between the steps, the apparent coordinates of all events (including those on the world line of a light signal) get shifted, so the light seems to jump ahead or back. Taking the limit of these approximations leads to the conclusion that the light signal does not seem to have constant velocity from the point of view of the accelerated observer. (Since the “frame jumps” lead to coordinate changes that are proportional to the distance of the event from the observer, this does not change the fact that every light signal seems to have the same speed when it reaches the observer, so there is no local change and it is just when the signal is far away from the observer that its velocity appears to vary.)

Source: (1001) Alan Cooper’s answer to A rotating frame can be divided into an infinite number of infinitesimal inertial frames. According to SR (special relativity) the light speed in each inertial frame is constant. Is light speed therefore constant in say the Sagnac experiment with SR? – Quora