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Sinnie

Light clock - basic explanation needed

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Hi all,

Apologies if this is not the right level of question - I have no education in cosmology whatsoever, but I have now been to several events at which the light clock experiment (and therefore time dilation) is explained. I understand it all, in principle, but can not get my head around exactly why that means that time is actually going slower for the faster moving clock/people. I've now read stuff online and watched Youtube videos and I know I'm missing some key part of understanding.

What I understand is that clock A (on earth) bounces a beam of light back and forth between two stationary (relative to the earth and our observer) mirrors. Each one is a tick and is 'normal' time. Clock B is on the spaceship, going for example, half the speed of light. Because the ship is moving so fast, from the observers perspective at clock A, the beam of light is in fact traveling at an angle, making a right angle triangle - the beam of light, whilst traveling at the speed of light, takes a longer journey in clock B than A and thus clock B ticks slower.

The resulting conclusion from this is that clock B runs slower, therefore time is running more slowly for the spaceship. But my initial conclusion would be that clock B is just reading the wrong time. Obviously my conclusion is wrong, but I don't understand the physics behind why I am wrong. This is where I'm hoping someone can break it down really simply for me to understand?

My (probably laughable) thought experiment to explain my thought process is:

You can simulate the physics of the light clock with people. Have two people act as the mirrors (A and B) and one person as the light (C). They all start at point X, with A and B standing 10 feet apart and the light (C) standing with A. Simultaneously, A and B run parallel in the same direction, at the same speed, whilst C runs from A to B and then back to A. This journey will be at an angle (as in the light clock). Have someone record each time C reaches A or B and stop when you reach 10, for example. At the same time, you can do the same thing with two stationary people - and of course, they will reach 10 sooner, as there is less distance to travel.

If we imagine that both beams of light (C) run at the same speed and it would take 6 seconds to cover the 10 feet between A and B, then the stationary clock will complete 10 ticks in 60 seconds. Therefore, after 60 seconds on the stationary clock, the moving clock will read something less (48 seconds, say). This just shows that the moving clock is incorrect - a product of physical distance. Would we actually say that those people running experienced less time?

A further mechanism to test this is to have two perfect mechanical machines that can not fail in any way. Each will make a mark on a piece of paper, in what is defined as 10 seconds (but is in fact mechanical working that takes 10 seconds). If you attached one of these devices to person C, in the moving clock - how many marks will be on the paper once the stationary clock reaches 10 ticks (60 seconds) - where the moving clock would have only recorded 8 ticks (48 seconds).

My understanding of the theory is that the mechanical device should also record only 8 marks - but I'm completely missing the understanding of how the speed of the object physically impacts the physical working of the mechanical device. It would seem to me that both machines would record 10 ticks, but the moving clock would record 48 seconds (8 ticks).

Fundamentally, my thought was that yes, 'time' runs slower - but you can do the same amount of physical stuff.

 

Final question - the premise of the light clock is that the observer in the ship views their light as bouncing up and down - and not at an angle. But that isn't true? They know they are moving, so logically know that the mirror is never in the same place, so surely if they were to go back and plot the position of the mirror for each bounce, they would plot the exact same positions as the observer on Earth? It only appears to go up and down, but for neither observer is it actually doing that.

In fact - how does the light physically bounce at an angle to begin with? If two people held a mirror and bounced a beam of light and then ran, the light would just shoot off in a straight line and disappear off?

Thank you for anyone who can clear my head of this fog!

 

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Flip it around. Rather then thinking of the light clock moving with respect to the Observer, think of it as the observer moving with respect to the light clock.  The light clock is stationary and our observer is flying by it at some fraction of.    Of course, someone sitting next to the light clock will see the light go straight up and down.   The observer flying past, would see the light travel at an angle relative to himself.   

The other point is that both observers will measure the light as traveling a c relative to themselves. So while the observer with the light clock measures the light as going up and down at c. the one moving relative to it measures it as traveling at a angle, at c, and thus taking longer to make the trip between the mirrors.

You seem be hung up on the idea that there is some absolute meaning to the the word "moving".  There isn't, all motion is relative.  There is no way to say who is or is not "really moving".

If you have two light clocks in motion with respect to each other, A and B, each with their own observer, then observer A would measure  light clock A as ticking normally and light clock B as ticking slow, while observer B will measure light clock B as ticking normally and light clock A as ticking slow.

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Moderator Note

This thread has some excellent questions that while they are essential in cosmology, those questions are better suited for the Relativity forum. I will move the thread there, though I may also participate. 

 

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4 hours ago, Sinnie said:

 

The resulting conclusion from this is that clock B runs slower, therefore time is running more slowly for the spaceship. But my initial conclusion would be that clock B is just reading the wrong time. Obviously my conclusion is wrong, but I don't understand the physics behind why I am wrong. This is where I'm hoping someone can break it down really simply for me to understand?

 

This is one of the trickier questions that is asked by everyone (literally that takes the time to understand relativity).

What is the physics behind time dilation ie What causes time dilation ? This may be expressed in numerous ways and some rather unusual methods, however it is one of the more difficult concepts to grasp. So I will endeavour to supply a Heuristic explanation. 

 As you know in Newton's laws of inertia we have a key set of relations, the 3 laws of inertia. Now many new to relativity posters commonly think these laws have been superseded by relativity which is incorrect. In truth those laws are fundamental to understanding time dilation  and how time dilation works. Now I am often heard stressing the importance of paying attention to the definitions. This situation is one of the main reasons I do so. You've probably know that mass is involved with regards to time dilation. The two types of mass we are interested in is inertial mass and gravitational mass. However the common mistake is forgetting that mass in physics is defined as " Resistance to inertia change " as per those three laws I mentioned earlier. Another key definition often missed is that energy is "ability to perform work " Now if you think about those two definitions this will give you a more accurate picture of the equation

[latex] E=mc^2[/latex] put into a direct English translation.  "The ability to perform work is directly proportional to the objects resistance to inertia change multiplied by the square of constant c." 

 Now we have two types of mass that you described above. You have the observer on earth and the observer in a spacecraft. Each has a different type of mass. Gravitational mass and inertial mass. Each form of mass is a measure of resistance to inertia change however the causes is different in so far as which type of energy supplies the work to supply the resistance. ( for this I will apply the term potential energy to the gravitational mass terms and kinetic energy to inertial mass terms ).

 Now we need to examine another key term " Spacetime ". This is distinct from our 3d Galilean view of volume, in so far as we add a variable time dimension. so now our familiar 3d universe is now a 4d universe. [latex]{x,y,z}\rightarrow {ct,x,y,z}[/latex] where the ct coordinate gives us a unit of vector length. This places it on the same playing field as the vectors  commonly learn in classical trigonometry. However another feature of importance is in defining an interval. Spacetime curvature I will get into later.

  Now here is where we get into the term inertial frames, in SR the primary transformations involve inertial reference frames. Now lets carefully define what is an inertial frame. As per the above it is a frame where the events are at constant velocity ie freefall. There is no acceleration in either magnitude or direction. As per the laws of inertia above. It is also a frame where our vector mathematics work as per the Galilean transforms. If you have acceleration we must account for this in other ways in gauge symmetry terms a rotation called rapidity, suffice it to say additional calculations.

Ok so far ? lets hope so and push on to why I stressed the above. we can simplify the above by another key relation under relativity "the equivalence principle" [latex] m_g=m_i [/latex] gravitational mass is equivalent to the inertial mass. So now we can put all this together.

 In the case of gravitational mass the location (potential energy In physics, is the energy held by an object because of its position relative to other objects". ) in this case the observer on Earth compared to the location of the spaceship.  However what does this energy describe in this case ? well it describes the ability to perform work in terms of the binding energy at that location. The mass term at that location describes the locations ability to resist inertia change. If were are describing multiple locations in roughly the same potential we can define this under spacetime coordinates. (spacetime field). When conditions are similar enough that Newtons laws apply without significant time dilation we can use our everyday vector addition we grew up with ie Pythagoras theory without adding any additional terms or ratios of change.  The resistance due to mass directly affects the time coordinate in terms of the interval {ct} recall I mentioned vectors ? I also mentioned Newtons laws of inertia. key formula being applied [latex] f=ma[/latex] or any equivalent formula such as the coupling strength of a field. They are in essence the same except the fields involved. It takes more energy to achieve the same distance covered, the mass term is higher so 1 Newton of force will move the object less in a higher potential. This applies to all processes in the same potential conditions, it affects the rate at which all particles in the immediate locale interact. (hence the twin aging, different clock rates, rates of decay etc.) 

 You should be able to formulate how inertial mass relates to the mass in terms of its binding energy to the time interval used in coordinate form. It should also help understand why the Lorentz transforms apply to both the time axis and the x axis where the object is described as moving away from or towards the observer. see here for the transforms. Each transform describes the interval length (defined as a vector ) change between reference frames due to the mass terms influence.

recall as an object gains inertia it gains inertia mass...

Now spacetime curvature as promised. Think of this as a coordinate map with axis [latex] ct,x,y,z[/latex] when you have no curvature terms then Pythagous theory applies in the triangle identities. Angles on triangles will add up to 180 degrees. Our regular everyday vector commutation rules apply. We also have no appreciable time dilation so our coordinate axis are all identical and 90 degrees from one another. When you get time dilation affects however this no longer applies, the angles no longer add up to 180 degrees, this is due to the length contraction and time interval contraction. It is now skewed to the original symmetry (skew symmetric}. the amount of skew depends on those transforms in that link above. 

 Now spacetime under GR describes the freefall condition (constant inertia). This freefall condition has a further detail that of parallel transport. Instead of having 1 object drop , drop two or more. In the case of the Earth the centre of mass is at the centre of the Earth (roughly). So these dropped objects no longer fall parallel to each other they converge upon one another as they approach the centre of mass. Now depending on arbitrary choice we can say this is positive or negative curvature but that's really an arbitrary choice. The position the two dropped objects will diverge in the opposite case.

granted the above is largely a simplification however all the essential principles are there. The last example is an example of tidal force under GR.

 One of the things to remember is that under GR objects follow the shortest spacetime path, that path is mathematically defined from the above under a freefall symmetry basis. The curvature terms apply to the particle path or its worldline. Usually denoted by the separation distance [latex] ds^2[/latex]  this will contain the details on how those coordinate axis transform in regard to one another in describing the freefall world line of a particle. The convergence and divergence of said curvature will affect the parallel transport of multiple particles.

 An everyday analogy of the above, think of time dilation in much the same way as signal propagation delay in electronic circuits. Where the signal can be delayed as it passes by an EM field in the right alignment. The physics behind the two is very similar. the constant c isn't simply the speed of light it is also the restriction of all information exchanges between any two points or particles.

Edited by Mordred

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On 2/11/2019 at 12:45 AM, Sinnie said:

The resulting conclusion from this is that clock B runs slower, therefore time is running more slowly for the spaceship. But my initial conclusion would be that clock B is just reading the wrong time.

Trying the simplest explanation that hopefully is physically correct.

At the basis of special relativity stand the 2 postulates. For this purpose I switch the order, and reword them a little:

  1. the speed of light is the same for every observer
  2. when frames of reference move uniformly relative to each other, the laws of nature are exactly the same.

You already used the first postulate to understand that a light clock moving relatively to you is 'ticking' slower. So far so good. But now, we add a mechanical clock to the light clock. when both stand still from my point of view they tick in exactly the same pace. But what do I see when I look at both together, passing me with high speed? If it is true what you said, that the light clock is just wrong, then the mechanical clock and the light clock do not run in pace anymore. So I can conclude that both are moving, and I am not. When I travel with both together, and they would run out of pace, I could conclude that I am moving. But this is in contradiction with the second postulate. The light clock would run slower than the mechanical clock, so the laws of electromagnetism would be different for me.

So you need both postulates to understand why time, i.e. all processes, appear to slow down for an observer moving relatively to me.

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Just in case the OP is still monitoring this thread (he hasn't responded to any of the answers given so far), I rigged up some animations that might help clarify things:

Assume you have two objects traveling in opposite directions and passing each other.  At the moment they pass each other, a flash of light is produced from that point, like this:  A and B is our object and the expanding circle of dots is the leading edge of the light flash

Invariant1.gif.737787dafa9c2a2c7605da05644441d3.gif

This view is from a frame in which A and B are measured as moving in from the sides.

The OP seems to assume that for someone traveling with A or B, this same flash of light would behave like this for A:

absoluteA.gif.bf506241de6411fc88bc90710a755d63.gif

And like this for B

AbsoluteB.gif.d9df527ead9805d5575ce9ceeb656dab.gif

However, this is not what Relativity predicts (Nor what any experiment to date measures).

The key is in the first postulate.  When it claims that the speed of light is the same for every observer, it means relative to that observer as measured by that observer.   If a flash of light is emitted from the same point as the observer, the flash will expand outward at c from that observer in all directions equally.

So instead, for someone at rest with respect to A, that same flash of light behaves like this:

invariant2.gif.04bfc3c7a54a788ad9b59436432a537c.gif

And for someone at rest with respect to B like this.

invariant3.gif.c509d44fff4a09e6f9b329579c0e2221.gif

Keep in mind that these last to images are of the same flash of light as shown in the firast animation, just veiwed from different reference frames.

In the following post, I'll deal with how this effects the light clock scenario.

Edited by Janus

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Okay, now lets take the above and apply it to a light clock.  we will use two light clocks, again labeled A and B.  We will start the first "tick" of each clock while they are in the same spot, and they will then separate ( at 0.5c in this example) as we examine what happens with the light pulses for each light clocks.

The pulses represented by the Larger yellow dots, while the expanding circles represent how far the pulses could travel at c in any direction.  To keep things from getting too cluttered, I will delete these expanding circles once they are no longer needed to reference the motion of either pulse.

First we will consider events as measured by someone at rest with respect to A.

LGHTCLK_1.gif.a988d25b9ce733c6c7707b7a89961271.gif

Both pulses start off at the same point. A's pulse continues straight up, while B's pulse sets off at an angle in order to stay between B's mirrors. B's flash at any moment cannot be any further from its initial emission point Than A's flash is as they climb.  Thus A's pulse hit's it mirror first and begins it return journey before B's pulse does.  From A's frame, B ticks more slowly.

If we examine things from B's frame, keeping in mind what we covered in the previous post, we see this:

LGHTCLK_B.gif.09b3b1bd397c110bbb8e40cff0550356.gif

Again each pulse travels away from the emission point at c, but in this frame, it is the bottom mirror of B that is the center of the expanding circle of light,  and it is Light clock B that ticks slower.*   So the reason that each light clock sees the other light clock's pulse travel at an angle is that each light clock must measure its own pulse as traveling straight up and down between it own mirrors, and that relationship must be consistent between the two frames.

The next question might be,  " But why does the behavior of light time?" 

The answer is: It doesn't.  It isn't that light effects time, it that the very nature of time and space determines how light behaves.  The behavior of light is not the cause but the consequence.  We use light in these examples because it reveals the nature of space-time.

 

*You may note that in this animation A's light pulse doesn't quite maintain its alignment with Clock A. This is due to an error in how the the motion of the Light clock was rendered. It doesn't move at a constant speed but accelerates up to speed and then slows down.  This is the default for the program, and something I forget to correct before doing the final animation.  It's a small thing, and I didn't think it was worth the trouble to go all the way back to fix.

Edited by Janus

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Apologies - I have read the first few replies. The unfortunately reality is that my science knowledge is not very good, so I was going to have to put together a carefully considered reply - so I needed a bit of a run up to it.

Those animations look very useful - I will sit down when my brain is switched on and try and digest everyone's helpful answers and see if I can approach wisdom.

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Handy videos and a good work up Janus No worries Sinnie take your time to absorb the material.

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Thank you everyone for taking the time to explain this - and for generating some animations.

I am pretty sure that I understand why the clocks appear to run slow from the perspective of an observer (the final animation was very useful as I had not grasped why the stationary clock would also appear to run slow). To avoid a convoluted reply, I will not quote people directly, but one of my confusions was why does time pass slower as you move faster. I wonder if either: I have missed this part of understanding from the replies (Mordred, your reply may have covered this, but alas, my knowledge is not good enough to follow everything with clarify). Or the light clock example does not cover this particular phenomenon. But first, some follow-up questions on the light clock specifically:

1) Isn't the light bouncing back and forth (not at an angle) only an illusion for both observers? Even if you set the clock on a table on Earth, the Earth is moving and rotating, so the path the light takes is not directly up and down - even though it appears to. If both the observer on Earth and on the spaceship were to take a map of the night sky and plot the path of the light of the clock in the spaceship (as in the above animations) based on where the ship was each time it hit the mirror - would they plot each 'tick' at the same point in the sky? Maybe this is a pointless question, but I feel that what is actually physically happening is that the light is bouncing at an angle for the observer in the spaceship, they just don't see it.

To approach it from another angle - there is a certain amount of 'physical action' occurring. The light does physically bounce at an angle, independent of who observers it and from where. Is that right? Does that not play into the scenario at all? Or is that cancelled out in the scenario?

2) This is a stupid question, but, how does the light bounce diagonally? If the light hits the mirror dead on, it will bounce back on the same path and miss the top of the clock, which has now moved. Or is the light purely metaphorical in this example? I know it's not relevant to relativity at all, it's just bugging me.

3) I fully get the each clock will appear slow from the perspective of the other observer. But that now throws a big question for me. Let's assume that the stationary clock has absolutely no velocity at all (not even planetary rotation). In a crude way, we can consider this recording 'true' time, as there will be no relativity effects from it's own movement. Apologies if this analogy butchers all known science, I just find it useful to use a concrete frame of reference. In any case, our moving clock will appear to tick slower from an observer at our stationary clock and vice versa. You then bring the clocks back together and the moving clock shows less time to have elapsed. So is the stationary clock appearing to run slower for the observer on the ship purely an illusion? Time does run slower for the observer on the moving ship, but time is evidently not running slower for the observer at the stationary clock - it just appears that way due to the behaviour of the light. Would the moving observer see their clock at 22:00, look at the stationary clock and think it says 17:00, then put them together and see that the stationary clock is in fact reading 05:00? Or have I completely missed this point?

 

OK, on to my remaining point of confusion. Janus ended their post by saying that this behaviour does not affect time. I presume they mean, the classical point, that if you travel really fast, you age slower. Do you just mean that the light clock analogy does not explain this behaviour? Or that moving fast does not make 'time slow down'?

To go back to my original analogy:

4) If you have two perfect mechanical machines that make a mark on paper every 10 seconds (defined by the workings of the machine, not by a measurement of 'time'). One machine with each clock. If you stopped both clocks and both machines when the stationary clock reach 60 seconds, which of these is true?

       a) Stationary clock reads 60, stationary machine has 6 marks, moving clock reads 30 (for example) and moving machine has 3 marks

       b) Stationary clock reads 60, stationary machine has 6 marks, moving clock reads 30 (for example) and moving machine has 6 marks

The essence of my question is - regardless of how fast you are going, can do you do the same amount of physical stuff? The 'faster you go, slower you age' idea suggests that you do less stuff and the machine would have 3 marks. If that is the case - can someone explain why? How can the speed you go physically alter the amount of physical effort that be completed? I'm guessing there is an additional component needed to explain this.

5) After having just watched Interstellar and being to a Brian Cox talk, I feel I have a good beginner understanding of black holes. Brian's use of the light cones actually, for the first time ever, showed me exactly why light can't pass out of the event horizon. So, there is time dilation caused by a black hole - but the additional explanation given here is gravity, which 'bends/pulls/stretches' space/light/time - thus making the distance to be covered larger than can be covered in the time - or something to that effect. My question is, how does the gravitational effect match onto the light clock? Is it the same effect and that gravity also lies underneath the light clock explanation? Is it the same principle, just applied differently? Or is it two different ways of getting to relativity? Again, I feel like I'm on the wrong track here.

 

Final, unrelated question, but this bugged me when Brian Cox explained it. The universe being flat - very briefly, I completely followed the principle that if you measure 3 points, you get a triangle and if the angles add up to 180, then it's flat. Less than 180 and it's saddle shaped, more than 180 and it's more spherical. I also get the caveat that the slice of space we're looking at is so tiny, it just looks flat.

To preface the question - I have no real understanding on the geometry of space, so I'm probably visualising this all wrong, however...

6) The universe is obviously 3D and we pick 3 points in space to do our triangle. But if you are inside a square, rectangle, pyramid, saddle, sphere or whatever and you don't know where the sides are and therefore any points you pick are inside the shape and not on the surface then surely it's all flat, whatever way you slice it? 99.99% of the slices you can take out of a sphere will be flat - it's only if you include 2 points on it's surface that you will get a curve? My guess is that it's not just the idea of the shape of the universe being flat, but that actual construction of the universe. Are we saying that in a saddle shape universe that what appears to be a straight line is in fact concave? If you bore a straight line through an apple, that line is straight, even those the surface is not - would that same bore hole be curved in a non-flat universe?

Maybe I should have studied more Physics at school...

 

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Here this will help on the Universe geometry question. Recall I mentioned parallel transport of light beams above. The curve is the path those light beams follow. They follow this path from another principle in Physics that being the path of least action. Which correlates how potential energy and kinetic energy (defined above) affect the geodesic equations provided on the second page. The first page describes the mass density distribution in how they are used to define the curvature (mass density curves spacetime). The slices seen on page two are simply the manifold with which the light paths follow. That manifold only depends on the beginning and end points of the light path (wold-line).

http://cosmology101.wikidot.com/universe-geometry

http://cosmology101.wikidot.com/geometry-flrw-metric/

Now onto the time dilation aspects, various fields can cause delays in how fast various signals and processes occur, the term we use to describe this is typically the mass term. This term also represents how strongly a particle couples to a field (binding energy) in a higher gravity potential the binding energy of all particles is stronger so it requires greater energy to go from point a to point b. The same occurs when the particle itself gains energy it also gains greater binding energy. So in each case either the field or the particle has a higher binding energy which slows down the rate f information exchange between particles.

As time is treated as a coordinate under spacetime it has a unit of length defined by [latex] ct[/latex]. So due to the binding energy this interval will decrease in length (Lorentz length contraction) due to the mass binding energy. This is time dilation in a nutshell, the length of the time interval in units of length decreases. So the particles take longer to travel the same distance to react with other particles. 

However keep in mind I am avoiding a lot of the math, and as such having to describe the processes above as simply as possible. When you get into the math and how vector relations transform under spacetime curvature the above becomes far clearer.  

Here this may help, this article details spacetime diagrams and will also help better understand the animations posted by Janus. There is extremely minimal mathematics in it as it doesn't include the transformation formulas of Lorentz just describes them under graph.

https://web.stanford.edu/~oas/SI/SRGR/notes/SRGRLect3_2015.pdf

this link explains a bit better the correlation between these diagrams and how they correlate to clock ticks with different observers

http://www.slimy.com/~steuard/teaching/classes/spacetime.pdf

explanation with the relevant math 

https://www.farmingdale.edu/faculty/peter-nolan/pdf/relativity/Ch03Rel.pdf

Edited by Mordred

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15 hours ago, Sinnie said:

Thank you everyone for taking the time to explain this - and for generating some animations.

I am pretty sure that I understand why the clocks appear to run slow from the perspective of an observer (the final animation was very useful as I had not grasped why the stationary clock would also appear to run slow). To avoid a convoluted reply, I will not quote people directly, but one of my confusions was why does time pass slower as you move faster. I wonder if either: I have missed this part of understanding from the replies (Mordred, your reply may have covered this, but alas, my knowledge is not good enough to follow everything with clarify). Or the light clock example does not cover this particular phenomenon. But first, some follow-up questions on the light clock specifically:

1) Isn't the light bouncing back and forth (not at an angle) only an illusion for both observers? Even if you set the clock on a table on Earth, the Earth is moving and rotating, so the path the light takes is not directly up and down - even though it appears to. If both the observer on Earth and on the spaceship were to take a map of the night sky and plot the path of the light of the clock in the spaceship (as in the above animations) based on where the ship was each time it hit the mirror - would they plot each 'tick' at the same point in the sky? Maybe this is a pointless question, but I feel that what is actually physically happening is that the light is bouncing at an angle for the observer in the spaceship, they just don't see it.

To approach it from another angle - there is a certain amount of 'physical action' occurring. The light does physically bounce at an angle, independent of who observers it and from where. Is that right? Does that not play into the scenario at all? Or is that cancelled out in the scenario?

2) This is a stupid question, but, how does the light bounce diagonally? If the light hits the mirror dead on, it will bounce back on the same path and miss the top of the clock, which has now moved. Or is the light purely metaphorical in this example? I know it's not relevant to relativity at all, it's just bugging me.

3) I fully get the each clock will appear slow from the perspective of the other observer. But that now throws a big question for me. Let's assume that the stationary clock has absolutely no velocity at all (not even planetary rotation). In a crude way, we can consider this recording 'true' time, as there will be no relativity effects from it's own movement. Apologies if this analogy butchers all known science, I just find it useful to use a concrete frame of reference. In any case, our moving clock will appear to tick slower from an observer at our stationary clock and vice versa. You then bring the clocks back together and the moving clock shows less time to have elapsed. So is the stationary clock appearing to run slower for the observer on the ship purely an illusion? Time does run slower for the observer on the moving ship, but time is evidently not running slower for the observer at the stationary clock - it just appears that way due to the behaviour of the light. Would the moving observer see their clock at 22:00, look at the stationary clock and think it says 17:00, then put them together and see that the stationary clock is in fact reading 05:00? Or have I completely missed this point?

The whole underlying issue with this is that you are assuming that there is such a thing as "absolute" motion.  That there is some way to say which of the light clocks is "really stationary" and which one is "really moving".   This is not the case.  There is absolute frame of rest against which all motion can be measured. Even the so-called "fixed stars" only provide a convenient frame of reference and not an absolute one.   So when we talk about the "stationary" light clock, we mean the light clock that is at rest relative to the frame from which we are considering at the time.   Thus in my animations above,  A is the "stationary" clock in the animation where it doesn't move in the animation frame and B is the "stationary" clock in the animation where it doesn't move in the animation frame.   This does not mean that we are looking at two different situations, just the same situation from different reference frames.

On point 2.  Once you give up on the idea of absolute motion, this doesn't become a issue.  Each light clock is equally allowed to treat itself as being "stationary", and thus having its light traveling straight up and down relative to its own frame.  Any other frame has to agree that the light stays between the mirrors of the light clock, and by default has to see the light pulse travel at a diagonal relative to their frame. 

Don't get too hung up on how you think light "should" behave.  We have to deal with the universe on its own terms.  Light does behave as described, and this behavior has been verified by real experiments.   We need to accept this, and use it to help us understand the universe around.

To address point 3 concerning what happens if you bring the Clocks back together, you have to consider more than just time dilation.  Length contraction and the Relativity of simultaneity Also are involved.  I won't go into the details here, but will say that what happens when the clocks are brought back together depends on how the clocks are brought back together.  To do this, one or both of the clocks will have to accelerate, and acceleration opens a whole new can of worms. 

15 hours ago, Sinnie said:

OK, on to my remaining point of confusion. Janus ended their post by saying that this behaviour does not affect time. I presume they mean, the classical point, that if you travel really fast, you age slower. Do you just mean that the light clock analogy does not explain this behaviour? Or that moving fast does not make 'time slow down'?

What I was saying is that the behavior of the the Light in the light clock experiment is not the cause of the time dilation. It is a symptom of time dilation.   The behavior of the light in the experiment is revealing something fundamental about the very nature of time and space.   The experiment could be done with a bouncing ball, and would still give the same results.  The point of the matter is that it isn't the light itself that is important, but the speed, c, that which it travels, and what the fact that such an invariant speed exists tells us about the universe we live in. 

 

16 hours ago, Sinnie said:

4) If you have two perfect mechanical machines that make a mark on paper every 10 seconds (defined by the workings of the machine, not by a measurement of 'time'). One machine with each clock. If you stopped both clocks and both machines when the stationary clock reach 60 seconds, which of these is true?

       a) Stationary clock reads 60, stationary machine has 6 marks, moving clock reads 30 (for example) and moving machine has 3 marks

       b) Stationary clock reads 60, stationary machine has 6 marks, moving clock reads 30 (for example) and moving machine has 6 marks

The essence of my question is - regardless of how fast you are going, can do you do the same amount of physical stuff? The 'faster you go, slower you age' idea suggests that you do less stuff and the machine would have 3 marks. If that is the case - can someone explain why? How can the speed you go physically alter the amount of physical effort that be completed? I'm guessing there is an additional component needed to explain this.

Again, you are going to have to provide more details as the the particulars of the experiment.  For instance, you say that both clocks are stopped when the "stationary" clock reads 60, but you don't say which reference frame this determination is being made from.     If it is from the "stationary" clock frame, then it has marked off 6 marks and the "moving"* machine will have marked off 3.    However, if being judged from the "moving" machine frame, then the "stationary" clock doesn't read 60 until the "moving" clock read 120, and thus the "stationary" machine will have 6 marks and the "moving" machine 12.

This is an example of the "relativity of simultaneity" I mentioned earlier.    The "stationary" clock and "moving" clock will not agree as to what events are simultaneous. For example, the "stationary" clock will say that it reading 60 and the "moving" clock reading 30 are simultaneous events.    However, the " moving" clock will say that when it reads 30, the "stationary" clock only reads 15.   Thus if you insist that both the "moving" and "stationary" machines stop running when the "stationary " clock read 60 according to the "stationary" clock's frame, Then in the "moving" clock's frame, the two machines do not stop simultaneously.  The "moving" machine stops working at 3 marks when its clock reads 30, but the "stationary" machine (whose clock reads 15 at this time), keeps running until it reads 60, and the "moving " clock reads 120, and then stops (at 6 marks).   So in one frame, the machines stop simultaneously, while in the other they don't**.  They'll never disagree as how many marks each machine made before stopping, but they will disagree as to whether or not the machines stopped at the same time.
 

16 hours ago, Sinnie said:

5) After having just watched Interstellar and being to a Brian Cox talk, I feel I have a good beginner understanding of black holes. Brian's use of the light cones actually, for the first time ever, showed me exactly why light can't pass out of the event horizon. So, there is time dilation caused by a black hole - but the additional explanation given here is gravity, which 'bends/pulls/stretches' space/light/time - thus making the distance to be covered larger than can be covered in the time - or something to that effect. My question is, how does the gravitational effect match onto the light clock? Is it the same effect and that gravity also lies underneath the light clock explanation? Is it the same principle, just applied differently? Or is it two different ways of getting to relativity? Again, I feel like I'm on the wrong track here.

 

The standard light clock experiment is purely Special Relativity and assumes flat space-time.   Gravity only comes into play if you have curved space-time and is the realm of General Relativity. 

*(I really hate using the terms "stationary" and "moving", as they imply a absolute nature that doesn't exist. It is so much better to use more generic labels like "machine A" and "machine B")

** Not knowing about,or failing to take the relativity of simultaneity into account accounts to ~99% of the problems people run into when dealing with Relativity.   It really should be the first thing they tackle.   A good grasp of it will prevent a good deal of headaches later.

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