Understanding Light's Constant Speed in Special Relativity

[phellen]

Dear Forum members,

How does special relativity account for the fact that light retains its speed even for an object that is heading towards the light at say, almost the speed of light? I think that if I can understand this it will be a great help

Many thanks

 

[phinds]

Dear Forum members,

How does special relativity account for the fact that light retains its speed even for an object that is heading towards the light at say, almost the speed of light? I think that if I can understand this it will be a great help

Many thanks

Google "Lorentz transformation"

 

[HallsofIvy]

Of course, the Lorentz transformation" comes from the fact that "light retains its speed even for an object that is heading towards the light at say, almost the speed of light", that is accounted for by "experimental evidence", the basic reason for any fact in physics.

 

[Dale]

How does special relativity account for the fact that light retains its speed even for an object that is heading towards the light at say, almost the speed of light?

In our previous conversation I mentioned that you need to consider three relativistic effects together: time dilation, length contraction, and the relativity of simultaneity. For measurements of the two way speed of light, time dilation and length contraction are sufficient.

Consider this scenario: suppose that we have a rod of proper length 10 (in units where c=1). On one end is a flash bulb, a clock, and a detector, and on the other end is a mirror. The speed of light is measured by measuring T, the time on the clock between the flash and the refelction of the flash at the detector, and taking 20/T.

For such a device at rest the light reaches the mirror at t=10, reflects, and reaches the detector at t=20, and since the clock is at rest there is no time dilation so T=20. So c=20/20=1.

Now, for such a device moving at v=.6, it is length contracted so its length is 8. Accounting for length contraction the flash of light reaches the mirror at t=20, reflects, and reaches the detector at t=25, but because of time dilation, at t=25 the clock only measures T=20. So c=20/20=1.

 

[darkhorror]

Dear Forum members,

How does special relativity account for the fact that light retains its speed even for an object that is heading towards the light at say, almost the speed of light? I think that if I can understand this it will be a great help

Many thanks

I am not sure if of exactly what you are wondering. Are you wondering how spacetime changes to account for light being the same speed in inertial frames of reference? Or are you wondering something like this, in an object's frame of reference it's speed is 0, thus light is moving at the speed of light. Then in another frame the object is moving towards the light, in this frame of reference the object is closing on each other at faster than the speed of light.

 

[Nugatory]

Dear Forum members,
How does special relativity account for the fact that light retains its speed even for an object that is heading towards the light at say, almost the speed of light? I think that if I can understand this it will be a great help

In addition to the other suggestions you've gotten so far, you might want to google for "relativistic velocity addition". Here's the basic situation:

You see something moving past you at speed $u$ (that "something" could be the flash of light that you're chasing, in which case $u=c$). You're moving past me at speed $v$, close to the speed of light. How fast is that something moving relative to me? Intuitively, we expect the answer to be $u+v$, which creates a real problem if I'm also going to measure the speed of the flash to be $c$.

However, if you take into account all of relativity of simultaneity, time dilation, and length contraction, it turns out that the answer is not $u+v$, it is $\frac{u+v}{1+uv}$ and if you try it you'll see that it we both end up with the light moving at $c$. (I'm measuring time in seconds and distance in light-seconds, just so that the speed of light comes out to one and I don't have to clutter the equation up with a bunch of "c" terms)

 

[ghwellsjr]

How does special relativity account for the fact that light retains its speed even for an object that is heading towards the light at say, almost the speed of light?

In our previous conversation I mentioned that you need to consider three relativistic effects together: time dilation, length contraction, and the relativity of simultaneity. For measurements of the two way speed of light, time dilation and length contraction are sufficient.

Consider this scenario: suppose that we have a rod of proper length 10 (in units where c=1). On one end is a flash bulb, a clock, and a detector, and on the other end is a mirror. The speed of light is measured by measuring T, the time on the clock between the flash and the refelction of the flash at the detector, and taking 20/T.

For such a device at rest the light reaches the mirror at t=10, reflects, and reaches the detector at t=20, and since the clock is at rest there is no time dilation so T=20. So c=20/20=1.

Here is a spacetime diagram depicting your scenario. I am considering the speed of light to be one foot per nanosecond. The blue end of the rod has the flash bulb, the clock, and the detector while the red end has the mirror:

Now, for such a device moving at v=.6, it is length contracted so its length is 8. Accounting for length contraction the flash of light reaches the mirror at t=20, reflects, and reaches the detector at t=25, but because of time dilation, at t=25 the clock only measures T=20. So c=20/20=1.

Now we transform that frame to one moving at -0.6c which makes the rod move at 0.6c:

However, this scenario doesn't correspond with what the OP asked about. He was wondering about an object moving toward light, not one where the light was carried with the object. I will depict that scenario in the next post.

 

[ghwellsjr]

In this scenario, the light source is way in front of the rod off to the right. The blue end of the rod has a detector and a clock and the red end of the rod is a mirror. When the light from the front is detected, it starts the clock and when the reflection is detected from the mirror, the clock stops. The first frame depicts the object at rest:

​

Now we transform to a frame moving at -0.6c so that the rod is approaching the light:

 

[ghwellsjr]

Now if you really want to approach the speed of light, here is the rest frame of a scenario similar to the preceding except that eventually, it will be going at 96%c:

I want to point out that the no one can see a flash of light approaching them until it gets to them. If they want to measure its speed, they have to start a timer when it first reaches them and then let it bounce off a mirror situated behind them and finally they have to stop the timer when the reflection gets to them. They can then calculate the speed of light to be 2*(7 feet/14 nsecs) = 1 foot per nanosecond.

Now let's transform to a speed of -0.96:

Note that all the events that were present in the rest frame are also present in the high speed frame of the object.

Any questions?

 

[phellen]

Thanks Guys this is great, I'm going to print this out and read through! Dark horror I was wondering the second part. Ghwellsjr what you said about measuring the speed of light is invaluable..

Thanks again

 

[phellen]

Dear ghwellsjr, thank you for depicting the scenario whereby the rod travels toward a beam of light (this is the one that really gets me). I just have a few questions (apologies). Regarding the method of measuring the speed of light, could the rod have synchronized clocks at the front and the back? ie could the light be measured purely by a one way journey between synchronized clocks? If not is this because of the simultaneity of relativity? Lastly, for these moving rods, they are time dilated yes, but does everything apart from the rod also suffer time dilation because of its motion relative to the rod? I believe that this is explained in the twin paradox and that it is the object which changes its rf (really accelerates) which encounters real time dilation. In this case is the apparent slowing of time witnessed by the twins purely an illusion?

ps those graphs are great, if you imagine them continuing through time (right up the page) it is quite useful.

Thanks

Paul

 

[ghwellsjr]

Dear ghwellsjr, thank you for depicting the scenario whereby the rod travels toward a beam of light (this is the one that really gets me). I just have a few questions (apologies). Regarding the method of measuring the speed of light, could the rod have synchronized clocks at the front and the back? ie could the light be measured purely by a one way journey between synchronized clocks?

Yes, but keep in mind that the method of synchronizing clocks involves sending light signals back and forth along with the information of what time is on the two clocks so that when you get all done, you end up with the same answer that you would get if you just reflected the light back to a single clock.

If not is this because of the simultaneity of relativity?

That is the reason. In other words, if two different observers with different speeds set up their own synchronized clocks or measure the round-trip speed of light using their own single clock and their own mirror at rest with respect to themselves, then they will both get the same answer for the speed of light coming from the same distant source.

Lastly, for these moving rods, they are time dilated yes, but does everything apart from the rod also suffer time dilation because of its motion relative to the rod?

I think it is more useful to think of things "suffering" Time Dilation that are moving according to a specified Inertial Reference Frame (IRF). The rod (or an observer with the rod) cannot directly see the Time Dilation of other moving objects unless he goes to all the rigamarole of making lots of measurements, applying the convention of simultaneity, doing a bunch of calculations and organizing it into the equivalent of a frame.

I believe that this is explained in the twin paradox and that it is the object which changes its rf (really accelerates) which encounters real time dilation. In this case is the apparent slowing of time witnessed by the twins purely an illusion?

What do you mean "illusion"? As I just said, no one can see the Time Dilation of other objects (or even their own). Illusions are things you can see.

When one of the twins accelerates, his speed can change in some IRF's and in those IRF's his Time Dilation changes but in other IRF's his speed does not change (the acceleration just causes a change in direction). If you always define a scenario in terms of a single IRF and apply Time Dilation to any object or observer that is moving then you can use the Lorentz Transformation (LT) process to see how the different objects have a different speed and therefore a different Time Dilation and you'll never have any confusion. If you try to figure it out without using the LT, you'll almost always end up with what seems like a contradiction or a paradox. This is actually the source of all the so-called paradoxes in SR, not sticking to a single IRF or not correctly transforming between different IRF's.

ps those graphs are great, if you imagine them continuing through time (right up the page) it is quite useful.

Thanks

Paul

You're welcome. And if you want to see lots of explanations for the Twin Paradox, do a search using my name and the word "diagram" or "twin".

 

[phellen]

Hi ghwellsjr, I was reading through some of the twin paradox pages and have discovered Doppler,

'Do you understand that looking at any activity while traveling away from it will make it appear to be in slow motion and while approaching, it will make it appear in fast motion? And do you know that this is called Doppler?'

I think that I have been confusing this with time dilation (prob mis read Brian Greene), this is the thing I was referring to when I mentioned illusions.

Im not fully there re the twin paradox, it still seems that time dilation (not Doppler) exists in virtue of acceleration/change in direction. But I will keep reading your posts.

Many thanks

 

[ghwellsjr]

Hi ghwellsjr, I was reading through some of the twin paradox pages and have discovered Doppler,

'Do you understand that looking at any activity while traveling away from it will make it appear to be in slow motion and while approaching, it will make it appear in fast motion? And do you know that this is called Doppler?'

I think that I have been confusing this with time dilation (prob mis read Brian Greene), this is the thing I was referring to when I mentioned illusions.

Im not fully there re the twin paradox, it still seems that time dilation (not Doppler) exists in virtue of acceleration/change in direction. But I will keep reading your posts.

Many thanks

Doppler is not an illusion. It is real. In fact Doppler, which is what an observer actually sees, is what Einstein's theory of Special Relativity must conform to when it defines and specifies coordinate systems and the Lorentz Transformation process. It has to make sure that whatever all observers see, measure and directly observe as defined in one IRF, remains the same when transformed to any other IRF.

I didn't say that Time Dilation does not exist. I said that it depends on the IRF in which the scenario is described. It's just like speed. Speed also depends on the IRF in which the scenario is described. And when we transform to a different IRF, all the speeds can change. And since Time Dilation is a function of the speed of an object, it can change as well. But just like there is no sense in which speed is absolute, there is no sense in which Time Dilation is absolute. We can't say that the Time Dilation is applied just to one twin because he is the only one that accelerates.

 

[phellen]

We can't say that the Time Dilation is applied just to one twin because he is the only one that accelerates.

This is what I used to think but then, the returning twin is supposed to be younger when they meet back up. So if B suffers time dilation according to the reference frame of A, and A suffers time dilation according to the reference frame of B, can they really have different ages when they are re-united. Most internet resolutions of this paradox seem to suggest that B is younger because in decelerating (according to one ref frame) or turning around (according to A's reference frame), B suffers greater time dilation according to A's rf.

I have some more books coming in the post, It takes me a long time to grasp this stuff..

 

[Nugatory]

Most internet resolutions of this paradox seem to suggest that B is younger because in decelerating (according to one ref frame) or turning around (according to A's reference frame), B suffers greater time dilation according to A's rf.

Many sources do indeed suggest exactly that resolution, but it is somewhat misleading. The acceleration is important only because it means that the situation is not symmetrical: A has a different experience than B, so it's not illogical or paradoxical that A has a different outcome than B. That's true, but it's not a complete resolution; it doesn't tell us how A's and B's outcomes will be different, nor why the difference should take the specific form that it does, with A being more aged than B. To answer those questions you have to trace their paths through spacetime using ghwellsjr's diagrams or equivalent.

The path-following also helps clarify the difference between time dilation (something that we say about a remote clock moving relative to us) and differential aging (the difference in proper time measured on different paths through spacetime between the same two events).

 

[phellen]

Thanks Nugatory,

Am I right in supposing that when the twins meet back up, they have different ages because of differential aging? (fingers crossed)

 

[Nugatory]

Thanks Nugatory,

Am I right in supposing that when the twins meet back up, they have different ages because of differential aging? (fingers crossed)

Yes.

 

[phellen]

Excellent :)