Speed of Light: Time and Motion Explained

[Worzel]

I keep reading that no object can travel faster then the speed of light and that the speed of light is constant.

If I am traveling along a road at 100mph and I switch on my headlights, the light would leave my car at the speed of light. However, to a person standing on the side of the road, the car would pass them at 100mph, with the light going away from the car at the speed of light. Therefore, relative to them, the light from the car must be traveling 100mph faster then the speed of light. I hope I explained that correctly.

So why is that not the case?

 

[Mentz114]

Everyone always sees light traveling at c m/s. That is, if they made measurements, they always come up with the same number. There are lots of topic threads about this subject in this forum. There might be some useful stuff in the FAQ.

 

[Naty1]

Everyone does measure light at the same fixed speed, c in the absence of gravity. That was one of Einstein's GREAT insights. It is NOT obvious, but IS experimentally verified so we know it to be true to a high degree of accuracy. It does NOT match everyday experience, just like a number of things in quantum theory do NOT match everyday experience.

Einstein also showed that space and time are NOT fixed...for the prior 3,000 years or or so of science I doubt few people even thought of that let alone believed it. So light speed is constant, but space and time are NOT constant! That's still amazing.

No one know WHY the speed of light is always observed, in the absence of gravity, at speed c. It's analogous to asking "why does an electron have the charge and mass we measure"?? nobody knows where any of the constants in nature come from.

 

[Worzel]

Hi Mentz114

Thank you for your answer but I already new that. So the question still needs to be answered.

Let me rephrase it. The light leaving the car must be traveling at the speed of light plus the speed of the car (100 mph). Ie. 2+6=8

However, if the person on the side of the road had the right equipment, they would only measure the light traveling at the speed of light. That is like saying that 2+6=6.

If the speed of light remains constant for the person driving the car and the person on the side of the road. Has something else changed and if so what.

 

[Ich]

The light leaving the car must be traveling at the speed of light plus the speed of the car (100 mph).

No. Look again:

If I am traveling along a road at 100mph and I switch on my headlights, the light would leave my car at the speed of light.

Be aware that "traveling along a road at 100mph" is a velocity measured relative to the road, while "the light would leave my car at the speed of light." is a velocity measured relative to the car.
So your adding 100 "road miles per road hour" and "670 616 629 car miles per car hour".

Obviously your tacit assumption "road miles = car miles and road hours = car hours" leads to a result that is contradicted by experimental evidence.

The necessary - if bold - thing to do is to drop the assumption of absolute space and time. That was the beginning of SR.

IOW, 2 roadmph + 6 roadmph = 6 roadmph is definitely wrong. But there is nothing wrong with 2 roadmph + 6 carmph = 6 roadmph. It just means that 6 carmph = 4 roadmph in this case.

 

[Tac-Tics]

Let me rephrase it. The light leaving the car must be traveling at the speed of light plus the speed of the car (100 mph). Ie. 2+6=8

The bolded part is a bad assumption.

Mechanical waves, like you already understand, move at a constant speed relative to the medium through which they travel.

Light is weird. It moves at a constant speed. Period. Consider this setup. I am on a straight race track. You are in the stadium. When the race starts, I shoot out a beam of light and start zipping down the race track at half the speed of light.

We both use our stop watches and record what we see one minute into the race.

To you, I am half a light minute out from the race track. The beam of light, moving at the speed of light (twice as fast as me), is one light minute away from the track. The distance between me and the beam of light is one half light minute.

From my perspective, things are different. While I still see myself a full light minute from the starting position, I see that the light was traveling at the speed of light relative to my position. This means the light beam, is one light minute away from me, but a total of one and a half light minutes away from the starting point.

How do you reconcile this? How can the light be two places (one light minute from the start and one and a half light minutes from the start) at the same time?

The answer is special relativity.

The most notable feature of special relativity is the idea of two things happening "at the same time" doesn't make sense.

 

[DrGreg]

Let me rephrase it. The light leaving the car must be traveling at the speed of light plus the speed of the car (100 mph). Ie. 2+6=8

To expand on what Ich said, in relativity velocities v_AB and v_BC are "added" using the formula

$$v_{AC} = \frac{v_{AB} + v_{BC}}{1 + v_{AB} v_{BC} / c^2}$$​

See Velocity-addition formula.

 

[Worzel]

Hi Tac-Tics

That is a much better example then mine. I have tried to read a bit about Special Relativity (SR) but most of it is beyond me.

I have cut and pasted the next two paragraphs.

If, on a windy day, an observer was placed midway between two firecrackers and heard them at the same time they might not conclude that they went off simultaneously. Since the sound travels relative to the air (its "ether") a wind blowing from one firecracker towards the other will result in sound from one firecracker being "wind aided" while the sound from the other firecracker will be "fighting" the wind. The observer could then measure the speed of the two sound signals and, noticing the difference in speed and decide that the one which had slower sound speed must have popped first. Its sound had to travel the same distance as the faster-sound signal but since its sound traveled slower it must have popped first. To use the new operational definition with sound (which is not the same speed for all observers, at least when the wind blows) would throw out our previous understanding of simultaneity.

The definition with light signals suffers from no such flaw since both signals travel the same distance at the same speed, c. Thus if they arrive together they must have started at the same time. This definition is in accordance with any and all previous intuitive but non-operational definitions. Nothing has been lost.

The second paragraph has c. and the rate of time as constants. However, what if the rate of time is not a constant value but a value that changes relative to the speed an object is traveling. Motion could then effect time, like the wind effects how quickly the observer could hear a firecracker. The stronger the motion, the bigger the effect would be.

We both use our stop watches and record what we see one minute into the race.

We both start our stopwatches at the same time but when my stopwatch reads one minute yours reads 30 seconds. At that moment, we both see you half a light minute along the race track.

When your stopwatch reads one minute mine reads two minutes and we both see you one light minute along the race track.

How can the light be two places (one light minute from the start and one and a half light minutes from the start) at the same time?

The light is not in the same place at the same time. The light is at the same moment in time for both of us but at different times for both of us. You are travailing through time at half the rate I am or I am traveling through time at twice the rate you are.

Well that is how it is in my mind but it cannot be that easy, can it?

 

[Mentz114]

...but a value that changes relative to the speed an object is traveling.

An inertial object hasn't got any speed. It's always at rest in it's own frame. It only appears to be moving from certain other points of view. There's no absolute speed, only relative speed. Relativity happens to other people.

It is true that clocks appear to run slowly when observed from a moving frame, but that's not actually important. What's important is that clocks show the Lorentzian length of a journey through space-time, and all observers agree on this elapsed time.

 

[Worzel]

The light is not in the same place at the same time. The light is at the same moment in time for both of us but at different times for both of us. You are travailing through time at half the rate I am or I am traveling through time at twice the rate you are.

So that was half right and half wrong. When my stopwatch reads one minute Tac-Tics will read less then one minute and when his reads one minute, mine will read more then one minute. What each others stopwatches read when ours reads one minute, can be worked out by using the Lorentzian Factor.

Did I get that right?

 

[HallsofIvy]

So that was half right and half wrong. When my stopwatch reads one minute Tac-Tics will read less then one minute and when his reads one minute, mine will read more then one minute. What each others stopwatches read when ours reads one minute, can be worked out by using the Lorentzian Factor.

Did I get that right?

What you said is not clear and whether you are right or wrong depends on the things you have not said. You have to distinguish who is observing the watches- that is, in what frame of reference the "measurements" are being made. What you say is true if you are the one observing the watches. If Tac-Tics is moving very fast relative to you then you will see his watch moving slower than yours- when yours reads one minute, you will observe Tac-Tics stop watch as reading less than one minute. When you see Tac-Tic's stop watch reading one minute, you will see yours reading more than a minute.

But who is moving and who is not is "relative". Tac-Tics is NOT moving relative to his own frame and he observes you moving very fast relative to his frame. For him the situation is reversed- when his watch reads one minute, he will observe your watch as reading less than one minute and when he observes your watch reading one minute, he will observe his own watch reading more than one minute.

 

[Worzel]

Hi HallsofIvy

The stadium I am sitting in, is in space and there is nothing else around that could have a gravitational effect.

But who is moving and who is not is "relative". Tac-Tics is NOT moving relative to his own frame and he observes you moving very fast relative to his frame. For him the situation is reversed

That is a bit like me standing by the side of an athletic track and getting out of breath just as much as the runners going round the track.

Anyhow, I was looking at it with me being stationary and with Tac-Tics being the one that is moving. So did I get it right?