# Light Clock Experiment - questions from a newbie?

• pd3000
In summary, the conversation revolves around understanding particle physics and time dilation. The use of examples such as the light clock experiment and the concept of frame of reference are discussed. A question is raised about what would happen if the observer in the experiment is also moving at close to the speed of light. It is clarified that in their own frame of reference, neither the observer nor the clock are moving faster than the speed of light, and that the concept of frame of reference is important. The conversation also touches on the expansion of space and its effect on the perceived speed of galaxies.
pd3000
Hi all, firstly, I must apologise for my level of physics knowledge and how this might be reflected in my question and the terminology used. I am trying to understand particle physics at an advanced age my neurons are not as elastic as they once were!

I have been listening to an excellent audio book by Brian Cox and Jeff Forshaw (Why does E=MC2), and for those relatively new (no pun intended!) to the subject, it uses some excellent examples to make this topic quite accessible.

The latest chapter explains time dilation using the light clock experiment as an example. I found this a really good example, having previously having had this explained, very confusingly, with the use of aeroplanes and atomic clocks! So, now I think I get it, and the implications this has for interstellar travel at light speed, but it raises a bunch of aditional questions for me that I'm hoping someone can explain.

In my mind I can envisage a subtle change to the experiment which causes me great consternation. Imagine for example, that instead of being stationary the 'observer' of the train carrying the light clock is also aboard another train moving paralllel to the clock carrying train and both trains are moving in diametrically opposite directions at close to the speed of light. In this example, the pythagorian mathematics which are the root of the calculations here suggest that the fleeting glimpse the observer sees of the clock is now so small that the light particle takes a path along the hypotenuse which is now so long that the mathematics must change immeasurably?

In the above example, if both trains are traveling at close to light speed, their separational speed must be nearly twice the speed of light? Is this a possible, or even logical conclusion?

Firstly, I know that special relativity tells me that "The speed of light is the same for all observers, no matter what their relative speeds". This is all well and good, but surely this means that each train in my example is now limited to half light speed in order to obey Newtonian physics? Does this also mean that any particle traveling across interstellar distances is also limited to half light speed just in case there is another particle taking a diametrically opposite path an 'observer' might be onboard one of these particles?

This also, to me, seems to restrict particle movement in a theoretically folded space time fabric (maybe this is a bit off topic). Let me use an example of my own. A photon is emitted from a distant star which I have measured to be one light year away, I can expect it to reach me at a predictable time because I know the distance, and the speed of light. What if the particle traverses previously unseen folded space and manages to reach me more quickly? Has it traveled more quickly than the speed of light, because I observe it to reach me more quickly, or must I factor in some distance differential? I know that there are arguments which suggest the folding of space time is possible, but would my previous example prove this one way or another as we would see light reaching us from previously known objects at different speeds depending on where they are in a warped space time fabric?

Apologies for the tangential last question, it just jumped into my head as I was writing.

As I said at the start, please be gentle with me, the more I learn here the more questions seem to raise themselves, try to answer me in a simple 'example' based way if possible, and please redirect me to a more basic forum if my questions are not worthy. As Marvin the Paranoid Android would have put it, "It gives me a headache just trying to think down to your level !". Please don't give yoursleves an aneurism trying to answer in a way I might comprehend :-)

Thanks.

I can only be partially helpful.

There are galaxies far far away which are moving at well below the speed of light in an absolute sense (they CAN'T move any faster) but they are being moved away from us at a speed ABOVE the speed of light because of the expansion of space. This does not violate any principles because in their frame of reference they are not exceeding c.

FRAME OF REFERENCE is what's important here. Neither of your spaceships are moving faster than c in their own frame of reference, so no principle is violated and they are not constrained by anything other than c (and the amount of energy they can expend).

Nothing is constrained in its own frame of reference by what something else is doing in IT'S frame of reference.

@phinds, excellent, thanks for your clarification, I think that clears up at least a couple of my points.

I would still like to know if my subtle change to the light clock experiment is a valid one, and how it would fundamentally change the outcome of the time dilation? Does the fact that the 'observer' is moving diametrically to the clock instead of stationary (I know that fundamentally, nothing is stationary) change the way time is perceived to an even greater extent. Given phinds last advice, I guess that both clock and observer still have their own frame of reference, but as the observers frame of reference in my example now provides an even more fleeting view of the clock, the time dilation must be much greater?

pd3000 said:
@phinds, excellent, thanks for your clarification, I think that clears up at least a couple of my points.

I would still like to know if my subtle change to the light clock experiment is a valid one, and how it would fundamentally change the outcome of the time dilation? Does the fact that the 'observer' is moving diametrically to the clock instead of stationary (I know that fundamentally, nothing is stationary) change the way time is perceived to an even greater extent. Given phinds last advice, I guess that both clock and observer still have their own frame of reference, but as the observers frame of reference in my example now provides an even more fleeting view of the clock, the time dilation must be much greater?

I hesitated to give any further answer because I'm a newbie at this myself, but I THINK I can answer that ... but will expect more knowledgeable folks to jump in if I have it wrong.

If a spaceship traveling at .9c emits a light beam then that light beam becomes its own frame of reference and does not care where it came from. Since the OTHER spaceship is traveling at .9c, the beam will eventually catch up with it. Since the first ship will be even farther away the next time it emits a beam, it will take even longer to catch up to the 2nd ship, but it WILL still catch up. The implication of that is that yes, the time dilation does not become infinite but does get very large.

I COULD be wrong about this. The ships might move out of each others observational universe. As I said, I'm new at this.

GALAXIES move out of each others observational universe because the space between them increases. It now occurs to me that the expansion of the space between the ships would have an effect, so I guess they DO move out of each others observational universe. This relativity stuff makes my head hurt. I like it better when 1+1=2

pd3000, I'm willing to believe that the links provided by Mentz114 answer your questions. If you can read them and translate the answer into English, I'd be happy to hear it.

Thanks for the links. Rather over my head, but I suppose there are only a finite number of ways of explaining some of these principals ! I will reread several times and see whether the clouds start to clear.

@phinds

If I'm lucky enough to be reincarnated as a physicist, I'll be happy to share any insight ;-)

Moving to chapter 3 of the audio book this evening, so will probably have more questions tomorrow.

Thanks again.

pd3000, this was a very interesting question and helped me understand special relativity better. Here is your answer.

The problem with your assumption is that you assigned velocities to both spaceships and added them together. Relative velocities are not strictly additive under special relativity, especially when you get close to the speed of light. (Check Mentz's link to the http://en.wikipedia.org/wiki/Velocity-addition_formula" )

Consider the two spaceships A and B and a stationary space station S. A moves with speed vAS = .5c relative to S and B moves with speed vB,S = -.5c relative to S.

S - - - - - - - A-> - - - - <-B

This is the problem you described. We must ask, does A perceive B as traveling at the speed of light or greater? You concluded that it did, which ended up causing problems. We would find the following relation under Galilean relativity:

$$v_{B,S} = v_{A,S} + v_{B,A}$$

which is more or less true for relatively slow motion, but we must make this adjustment for speeds close to the speed of light:

$$v_{B,S} = \frac{v_{AS} + v_{BA}}{1 + \frac{v_{AS}v_{BA}}{c^2}}$$

Solving for vBA and plugging in .5c for vAS and -.5c for vBS,

$$v_{B,A} = \frac{-c}{1 - \frac{(-.5c)(.5c)}{c^2}} = \frac{-c}{1.25}$$

This quantity is thankfully always less than the speed of light, which relieves us of the difficulties you mentioned. Hope this helps.

Last edited by a moderator:
pd3000 said:
[..]
The latest chapter explains time dilation using the light clock experiment as an example. I found this a really good example, having previously having had this explained, very confusingly, with the use of aeroplanes and atomic clocks! So, now I think I get it, and the implications this has for interstellar travel at light speed, but it raises a bunch of aditional questions for me that I'm hoping someone can explain.

In my mind I can envisage a subtle change to the experiment which causes me great consternation. Imagine for example, that instead of being stationary the 'observer' of the train carrying the light clock is also aboard another train moving paralllel to the clock carrying train and both trains are moving in diametrically opposite directions at close to the speed of light. In this example, the pythagorian mathematics which are the root of the calculations here suggest that the fleeting glimpse the observer sees of the clock is now so small that the light particle takes a path along the hypotenuse which is now so long that the mathematics must change immeasurably?

In the above example, if both trains are traveling at close to light speed, their separational speed must be nearly twice the speed of light? Is this a possible, or even logical conclusion? [..]
I did not copy what you meant with immeasurably changing math, but the separation speed is no problem at all: in the system to which you refer, each train can go almost at light speed, and in opposite directions if you wish. By mathematical necessity, in that system their separation speed will thus indeed be almost 2c. However, from the perspective of a system in which one of the trains is in rest, the other train must of course still go at a speed less than c - no object can go as fast as light in vacuum.

Such a change of perspective corresponds with a system transformation; the appropriate formula that follows from the Lorentz transformation is called the composition of velocities equation. That has nothing to do with warped spaces or so.

Regards,
Harald

PS I see that the details of using the composition of velocities equation are nicely described in the preceding post

## 1. What is the Light Clock Experiment?

The Light Clock Experiment is a thought experiment used to explain the concept of time dilation in Einstein's theory of special relativity. It involves a clock consisting of two mirrors facing each other with a beam of light bouncing between them.

## 2. How does the Light Clock Experiment work?

In the Light Clock Experiment, the clock is set up so that the beam of light travels a fixed distance between the two mirrors. As the speed of light is constant, the time it takes for the light to travel back and forth between the mirrors is also constant. However, when the clock is in motion, the distance the light has to travel is longer due to the time dilation effect, resulting in a slower perceived passage of time.

## 3. What does the Light Clock Experiment prove?

The Light Clock Experiment proves that time is relative and is affected by the speed at which an object is moving. It also supports Einstein's theory of special relativity, which states that the laws of physics remain the same for all observers in uniform motion.

## 4. Are there any limitations to the Light Clock Experiment?

While the Light Clock Experiment is a useful thought experiment, it is not possible to construct a physical clock that operates in this way due to the limitations of technology. Additionally, the experiment only applies to objects moving at speeds close to the speed of light.

## 5. How is the Light Clock Experiment relevant in modern science?

The Light Clock Experiment is relevant in modern science as it helps us understand the effects of time dilation on objects moving at high speeds. It also plays a critical role in fields such as GPS technology, where precise timekeeping is necessary for accurate positioning. Furthermore, the experiment has led to further developments and advancements in the field of relativity and has been used to support other theories, such as the theory of general relativity.

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