Relativity

[fast]

Something just doesn't sit well with me. It seems to me that light has a universal maximum speed just like Einstein said. It's a universal constant, probably due to some causality principle, but my interpretation is unlike others.

If you are standing still and I walk by you at 2MPH and we both cut a light on at precisely the same time shining towards a building, the beams should reach their destination simultaneously despite our difference in speed. If a third person came up in a very fast jet (3000MPH) and all three lights are cut on, then never mind all this observer jazz. Light can only travel so fast. It's universal. It's a universal constant.

 

[skepticalbip]

Correct. Experiments have verified that, no matter who measures the speed of light in whatever reference frame and whatever velocity they are moving with respect to other reference frames, they will measure the speed of light at c. This means that the guy in the caboose in your thought experiment will see the light leaving his flashlight at c (with respect to the train) and someone standing by the tracks watching the train go by will also measure that light from the flashlight on the moving train traveling at c (with respect to himself) too.

This makes no sense in Newtonian mechanics (although a measured and tested reality) but was one of the problems in our understanding of reality that uncle Albert resolved with his theory of relativity.

I don't think you understand the magnitude of my mistake.

I certainly would not argue. Communication isn't really my strong suit.

I've watched garboodles of both regular videos and university lectures on the subject. I have a good sense of what's being explained. That's not the issue. The hard part has been over.

The disconnect for me has been the wording of the postulate, not the explanation. When I hear the words, "c is a universal constant," what I envision is one thing, but the explanations to follow are starkly contrasted.

It's like I'm being told that light is not subject to relativity followed by explanations showing that it is. I've been caught up in what appears to be a lexical ambiguity.

When I'm told that light is a universal constant, especially as a postulate to support a theory of relativity, I'm not thinking the universal constant itself is relative to observers as is everything else. Instead, I was thinking that the speed of light has a true maximum speed and so could not move faster. I know how that sounds. Yes, c relative to observer A flying fast cannot exceed c, and the same goes for observer G on the ground, but when observer A reports his findings to observer G, he might not have observed it, but he calculates that c exceeds c by speed of observer a, which violates what I thought the postulate was, a universal constant, but it's not a mere universal constant, is it? It's relative to the observers in such that c does not have a maximum but rather a maximum relative to the observer.

As I see the major problem, you seem to be attempting to make intuitive sense of relativity but relativity is not intuitive since all our life experience is seen more simply as Newtonian. If our life experience had been in an environment where everything was moving at relativistic velocities with respect to everything else then we would find relativity intuitive and Newtonian mechanics rather odd. Unfortunately, to really understand relativity, one must first master the model and be comfortable with the math.

It is possible that you are interpreting "the speed of light is a constant" as meaning something other than intended. It is a constant for any observer - all observers measure it at c regardless of the relative motions of the source or observer while other measurements will change with respect to relative motion of the objective and/or the observer.
An example:
Assume there is a space station with a rocket approaching from one direction at 0.7c with respect to the station and another rocket approaching from the exact opposite direction at 0.7c with respect to the station. Both rockets and the space station have bright lights.
The station will measure each rocket approaching at 0.7c and the speed of the light from itself and each rocket at c.
Each rocket will measure their closing velocity with the station at 0.7c, their closing velocity with the other rocket at 0.94c, and the speed of light from their rocket, the station, and the other rocket at c.

 

[bilby]

The problem is that humans don't move very fast, so they don't notice relativistic effects.

If two cars are traveling in opposite directions on a freeway, at exactly 50mph (relative to the road surface), then the drivers see the other car approaching at a tiny bit less than 100mph. But the tiny bit is far too tiny to detect with human senses, and is too small to measure with any but the most advanced equipment imaginable. Unless you want to spend billions of dollars on the world's most accurate speedometers, you simply cannot detect that the correct answer to the question 'what is the apparent closing speed of the other car' is, in reality, a bit less than the answer to the sum 50mph + 50mph = 100mph

The difference is tiny - the ratio of the product of the two approach speeds to the square of the speed of light. So when the approach speeds are a tiny fraction of light speed, the difference between (Newtonian) expectations and reality is tiny squared.

In the example above, the closing speed is actually about 99.99999999999987mph, and not the 100mph you might expect.

 

[Treedbear]

Something just doesn't sit well with me. It seems to me that light has a universal maximum speed just like Einstein said. It's a universal constant, probably due to some causality principle, but my interpretation is unlike others.

If you are standing still and I walk by you at 2MPH and we both cut a light on at precisely the same time shining towards a building, the beams should reach their destination simultaneously despite our difference in speed. If a third person came up in a very fast jet (3000MPH) and all three lights are cut on, then never mind all this observer jazz. Light can only travel so fast. It's universal. It's a universal constant.

I don't know if this will help or confuse matters more, but both observers will see the light from both lights moving at c. If I'm standing still I will see you moving at 2 mph in the same direction as the two light beams. Therefore I will see the two beams moving away from you at c minus 2 mph. That of course is not what you see which is the light beams moving away at a velocity of c. This is because time is moving slower for you than it is for me.

ETA: Conversely you will see the two beams moving away from me at c + 2 mph, simply because with no other reference point it will appear as if I am moving in the opposite direction from you and the light beams. No violation of c from your perspective but of course it's impossible from mine. This only makes sense if there is some previous and subsequent reference point at which we can both take account of all intermediate accelerations to determine which one of us experienced the net change in velocity and the resulting time distortion.

 

[Kharakov]

In the example above, the closing speed is actually about 99.99999999999987mph, and not the 100mph you might expect.

Are you sure it's not 100 mp1.00000000000000001h?

Light can only travel so fast. It's universal. It's a universal constant.

c is in an ideal vacuum (not in all materials).

light can appear to move faster than c in distant galaxies, due to spacetime expansion, but this is not related to local measurements of light in a vacuum.


Something that might help you think about it is that light from the moving jet will be blueshifted or redshifted (depending on if the jet is moving towards or away from the building). This means the energy/momentum the light transmits is increased or decreased, but the light travels at the same velocity.

So light has various "masses" (amounts of energy), but always travels at the same velocity. If I run towards you with a flashlight, the light has a little bit more "mass" to it than if I run away from you with a flashlight... but the light will traverse the same distance between us in the same amount of time no matter how fast we are moving relative to one another. The difference is only in the energy level of the light.

I shown the light on it.

 

[fast]

Something just doesn't sit well with me. It seems to me that light has a universal maximum speed just like Einstein said. It's a universal constant, probably due to some causality principle, but my interpretation is unlike others.

If you are standing still and I walk by you at 2MPH and we both cut a light on at precisely the same time shining towards a building, the beams should reach their destination simultaneously despite our difference in speed. If a third person came up in a very fast jet (3000MPH) and all three lights are cut on, then never mind all this observer jazz. Light can only travel so fast. It's universal. It's a universal constant.

I don't know if this will help or confuse matters more, but both observers will see the light from both lights moving at c. If I'm standing still I will see you moving at 2 mph in the same direction as the two light beams. Therefore I will see the two beams moving away from you at c minus 2 mph. That of course is not what you see which is the light beams moving away at a velocity of c. This is because time is moving slower for you than it is for me.

ETA: Conversely you will see the two beams moving away from me at c + 2 mph, simply because with no other reference point it will appear as if I am moving in the opposite direction from you and the light beams. No violation of c from your perspective but of course it's impossible from mine. This only makes sense if there is some previous and subsequent reference point at which we can both take account of all intermediate accelerations to determine which one of us experienced the net change in velocity and the resulting time distortion.

I always feel the observer element to be a distraction. What anyone observed from their respective frame of reference sidetracks the issue about the lights movement. If an instrument at the wall detects light as it arrives, it should be able to tell the order in which the lights beems arrived, irrespective of whatever varying accounts observers might report.

Let's race. Your space ship against mine. We're next to each other, but you let me take off first. I take off and reach top speed of 1/4c. You later take off and reach your maximum velocity of 1/2c. You're still behind me but catching up fast. At some point, you and I will be parallel given our linear vector.

At the point we are parallel, it becomes obvious that you're going to take me, so I say, let our lights race. You and I cut on our headlights at the precise moment you are next to me. If light indeed has a maximum velocity, our beems should run neck and neck and cross the finish line at precisely the same moment, but that's not what people are saying. They are saying you will see light shoot out at light speed, and I'll see my light shoot out at light speed, but let what we see be damned. What does the instrument at the finish line say? Our lights arrived simultaneously or yours arrived first?

 

[Treedbear]

Something just doesn't sit well with me. It seems to me that light has a universal maximum speed just like Einstein said. It's a universal constant, probably due to some causality principle, but my interpretation is unlike others.

If you are standing still and I walk by you at 2MPH and we both cut a light on at precisely the same time shining towards a building, the beams should reach their destination simultaneously despite our difference in speed. If a third person came up in a very fast jet (3000MPH) and all three lights are cut on, then never mind all this observer jazz. Light can only travel so fast. It's universal. It's a universal constant.

I don't know if this will help or confuse matters more, but both observers will see the light from both lights moving at c. If I'm standing still I will see you moving at 2 mph in the same direction as the two light beams. Therefore I will see the two beams moving away from you at c minus 2 mph. That of course is not what you see which is the light beams moving away at a velocity of c. This is because time is moving slower for you than it is for me.

ETA: Conversely you will see the two beams moving away from me at c + 2 mph, simply because with no other reference point it will appear as if I am moving in the opposite direction from you and the light beams. No violation of c from your perspective but of course it's impossible from mine. This only makes sense if there is some previous and subsequent reference point at which we can both take account of all intermediate accelerations to determine which one of us experienced the net change in velocity and the resulting time distortion.

I always feel the observer element to be a distraction. What anyone observed from their respective frame of reference sidetracks the issue about the lights movement. If an instrument at the wall detects light as it arrives, it should be able to tell the order in which the lights beems arrived, irrespective of whatever varying accounts observers might report.

Let's race. Your space ship against mine. We're next to each other, but you let me take off first. I take off and reach top speed of 1/4c. You later take off and reach your maximum velocity of 1/2c. You're still behind me but catching up fast. At some point, you and I will be parallel given our linear vector.

At the point we are parallel, it becomes obvious that you're going to take me, so I say, let our lights race. You and I cut on our headlights at the precise moment you are next to me. If light indeed has a maximum velocity, our beems should run neck and neck and cross the finish line at precisely the same moment, but that's not what people are saying. They are saying you will see light shoot out at light speed, and I'll see my light shoot out at light speed, but let what we see be damned. What does the instrument at the finish line say? Our lights arrived simultaneously or yours arrived first?

Simultaneously. As measured by the instrument and also as seen by either one of us.

 

[fast]

I always feel the observer element to be a distraction. What anyone observed from their respective frame of reference sidetracks the issue about the lights movement. If an instrument at the wall detects light as it arrives, it should be able to tell the order in which the lights beems arrived, irrespective of whatever varying accounts observers might report.

Let's race. Your space ship against mine. We're next to each other, but you let me take off first. I take off and reach top speed of 1/4c. You later take off and reach your maximum velocity of 1/2c. You're still behind me but catching up fast. At some point, you and I will be parallel given our linear vector.

At the point we are parallel, it becomes obvious that you're going to take me, so I say, let our lights race. You and I cut on our headlights at the precise moment you are next to me. If light indeed has a maximum velocity, our beems should run neck and neck and cross the finish line at precisely the same moment, but that's not what people are saying. They are saying you will see light shoot out at light speed, and I'll see my light shoot out at light speed, but let what we see be damned. What does the instrument at the finish line say? Our lights arrived simultaneously or yours arrived first?

Simultaneously. As measured by the instrument and also as seen by either one of us.

I agree, but others do not.

Consider the caboose example in the OP and the responses to it. If the train is traveling at the speed of light, the light on the caboose will not shine and light up the engine train, for the speed of light would have to travel faster than the caboose, and light cannot do that because that would require the speed the light is traveling to exceed c.

 

[Underseer]

"Believers in relativity"?

Seriously?

You would say that bout a scientific fact?

 

[Underseer]

Something just doesn't sit well with me. It seems to me that light has a universal maximum speed just like Einstein said. It's a universal constant, probably due to some causality principle, but my interpretation is unlike others.

If you are standing still and I walk by you at 2MPH and we both cut a light on at precisely the same time shining towards a building, the beams should reach their destination simultaneously despite our difference in speed. If a third person came up in a very fast jet (3000MPH) and all three lights are cut on, then never mind all this observer jazz. Light can only travel so fast. It's universal. It's a universal constant.

The Michaelson-Morley experiment shows that both observers will measure the same value of c for the speed of light.

Yes, it's counterintuitive. That's why so many physicists had such an emotional reaction to the Michaelson-Morley experiment.

Whether or not it makes sense to you is irrelevant. It is true, and it has been verified again and again by experiment.

 

[fast]

"Believers in relativity"?

Seriously?

You would say that bout a scientific fact?

Perhaps contrary to tone, I am not denying the implications of the general theory of relativity. I have concerns about a few of the statements regarding the facts. People believe in scientific facts, as they might ought, but not every bit of verbiage preached will therefore prevail under the alter of truth.

 

[Treedbear]

...
Simultaneously. As measured by the instrument and also as seen by either one of us.

I agree, but others do not.

Consider the caboose example in the OP and the responses to it. If the train is traveling at the speed of light, the light on the caboose will not shine and light up the engine train, for the speed of light would have to travel faster than the caboose, and light cannot do that because that would require the speed the light is traveling to exceed c.

You mean this part?

...
Now, cut the light off. The driver of the train speeds up to the speed of light. You cut the light back on to see the back of the engine car, but this time, no light shines on the back of it. Why? Because the light is traveling at its maximum speed and cannot move past the caboose. Apparently, some people think, and hence the confusion, that the light will shoot out relative to the person shining it. Not so.
...

I didn't comment at the time, but all bet are off when you suggest that the train travels at the speed of light. I'm not sure people realized that was the condition. I agree with you. Ain't gonna happen.

 

[bilby]

I always feel the observer element to be a distraction. What anyone observed from their respective frame of reference sidetracks the issue about the lights movement. If an instrument at the wall detects light as it arrives, it should be able to tell the order in which the lights beems arrived, irrespective of whatever varying accounts observers might report.

Let's race. Your space ship against mine. We're next to each other, but you let me take off first. I take off and reach top speed of 1/4c. You later take off and reach your maximum velocity of 1/2c. You're still behind me but catching up fast. At some point, you and I will be parallel given our linear vector.

At the point we are parallel, it becomes obvious that you're going to take me, so I say, let our lights race. You and I cut on our headlights at the precise moment you are next to me. If light indeed has a maximum velocity, our beems should run neck and neck and cross the finish line at precisely the same moment, but that's not what people are saying. They are saying you will see light shoot out at light speed, and I'll see my light shoot out at light speed, but let what we see be damned. What does the instrument at the finish line say? Our lights arrived simultaneously or yours arrived first?

Simultaneously. As measured by the instrument and also as seen by either one of us.

I agree, but others do not.

Consider the caboose example in the OP and the responses to it. If the train is traveling at the speed of light, the light on the caboose will not shine and light up the engine train, for the speed of light would have to travel faster than the caboose, and light cannot do that because that would require the speed the light is traveling to exceed c.

The train cannot travel at the speed of light. As an object with non-zero mass approaches light speed, adding more energy to make it go faster contributes to its mass, more than it contributes to its speed. Kinetic energy is proportional both to mass and to the square of velocity, so to add a bit of velocity to an already fast moving object you need to add a lot of energy, which means you also add a lot more mass, and as the velocity approaches light speed, the mass (and hence the extra energy required for further acceleration) approaches infinity. Unless you have infinite energy available, you can't accelerate an object with a non-zero rest-mass to light speed; and an object with zero rest mass (eg a photon) cannot travel at any other speed in a vacuum, because to do so would imply zero energy - and an object with zero energy and zero mass is equal to no object at all. Interestingly, this also means that from a photon's perspective, time doesn't exist - a photon that arises in a quasar at the edge of the observable universe, and that takes millions of years (as measured by us) to reach our telescope, will, from the perspective of the photon, have been emitted by the quasar and absorbed by the telescope's optics simultaneously, having traveled zero distance. To a photon, everywhere is the same place.

If the train is traveling at 99.999% of the speed of light (add any finite number of 9s after the decimal point), then the light on the caboose will travel at the speed of light - as measured by the guy on the caboose - and return to him, lighting up the locomotive; It will be just as if the train wasn't moving at all from his POV.

An observer next to the tracks will see the same thing - but the train will appear to be very much shorter than the guy in the caboose thinks it is, so the light will still travel from one end to the other in the same amount of time, despite only moving fractionally faster than the train itself.

If the train is accelerating, trying (futilely) to 'outrun' the light, then the observer next to the tracks will also see time slowing down to conserve the speed of light from all perspectives (and from the POV of the guy on the train, the guy next to the tracks get old a lot faster as time appears to speed up).

No matter what you do to try to make light speed appear different to different observers, each observer's measurement of length and/or time will adjust exactly enough to keep the measured light speed constant.

 

[skepticalbip]

Something just doesn't sit well with me. It seems to me that light has a universal maximum speed just like Einstein said. It's a universal constant, probably due to some causality principle, but my interpretation is unlike others.

If you are standing still and I walk by you at 2MPH and we both cut a light on at precisely the same time shining towards a building, the beams should reach their destination simultaneously despite our difference in speed. If a third person came up in a very fast jet (3000MPH) and all three lights are cut on, then never mind all this observer jazz. Light can only travel so fast. It's universal. It's a universal constant.

The Michaelson-Morley experiment shows that both observers will measure the same value of c for the speed of light.

Yes, it's counterintuitive. That's why so many physicists had such an emotional reaction to the Michaelson-Morley experiment.

Whether or not it makes sense to you is irrelevant. It is true, and it has been verified again and again by experiment.

Actually the shock of the Michaelson-Morley experiment to the physics of the day was that it was a null experiment. It was intended to measure the luminiferous aether but instead found it didn't exist. "Aether drag" could no longer be used to explain why the speed of light from sources moving at various velocities was always measured at the same speed. The answer to why c was always measured at the same speed was eventually provided by Einstein.

 

[fast]

Something just doesn't sit well with me. It seems to me that light has a universal maximum speed just like Einstein said. It's a universal constant, probably due to some causality principle, but my interpretation is unlike others.

If you are standing still and I walk by you at 2MPH and we both cut a light on at precisely the same time shining towards a building, the beams should reach their destination simultaneously despite our difference in speed. If a third person came up in a very fast jet (3000MPH) and all three lights are cut on, then never mind all this observer jazz. Light can only travel so fast. It's universal. It's a universal constant.

The Michaelson-Morley experiment shows that both observers will measure the same value of c for the speed of light.

Yes, it's counterintuitive. That's why so many physicists had such an emotional reaction to the Michaelson-Morley experiment.

Whether or not it makes sense to you is irrelevant. It is true, and it has been verified again and again by experiment.

I'm okay with the counterintuitiveness. I'd like to walk the road of facts whereever it might lead, whether I like it or not, but must I remain silent in the face of curiosity while quips are intimated my way? Surely it can withstand some probing from lil-o me.

I'm not so sure this ACTUAL experiment was designed with my shade of curiosity in mind. Do you not see the ambiguity in "both observers will measure the same value of c for the speed of light?"

If you are traveling at 1/4c, you will measure c as c, and if I am traveling 1/2c, I will measure c as c. Got it.

But, from this, you think what exactly? The bulb on the caboose is traveling at the speed of light, but let's slow it down by 1MPH and cut the light on, the photons emitted will now travel at c, but relative to you, it will take off slower than walking speed relative to the train carrying the bulb. Put the bulb on front of the engine car and bump the speed of the train up 1MPH until it reaches the speed of light. According to some, the light will take off and brighten our way, but my thinking is that relative to me, the light will not shine to light up our way.

 

[fast]

I agree, but others do not.

Consider the caboose example in the OP and the responses to it. If the train is traveling at the speed of light, the light on the caboose will not shine and light up the engine train, for the speed of light would have to travel faster than the caboose, and light cannot do that because that would require the speed the light is traveling to exceed c.

The train cannot travel at the speed of light. As an object with non-zero mass approaches light speed, adding more energy to make it go faster contributes to its mass, more than it contributes to its speed. Kinetic energy is proportional both to mass and to the square of velocity, so to add a bit of velocity to an already fast moving object you need to add a lot of energy, which means you also add a lot more mass, and as the velocity approaches light speed, the mass (and hence the extra energy required for further acceleration) approaches infinity. Unless you have infinite energy available, you can't accelerate an object with a non-zero rest-mass to light speed; and an object with zero rest mass (eg a photon) cannot travel at any other speed in a vacuum, because to do so would imply zero energy - and an object with zero energy and zero mass is equal to no object at all. Interestingly, this also means that from a photon's perspective, time doesn't exist - a photon that arises in a quasar at the edge of the observable universe, and that takes millions of years (as measured by us) to reach our telescope, will, from the perspective of the photon, have been emitted by the quasar and absorbed by the telescope's optics simultaneously, having traveled zero distance. To a photon, everywhere is the same place.

If the train is traveling at 99.999% of the speed of light (add any finite number of 9s after the decimal point), then the light on the caboose will travel at the speed of light - as measured by the guy on the caboose - and return to him, lighting up the locomotive; It will be just as if the train wasn't moving at all from his POV.

An observer next to the tracks will see the same thing - but the train will appear to be very much shorter than the guy in the caboose thinks it is, so the light will still travel from one end to the other in the same amount of time, despite only moving fractionally faster than the train itself.

If the train is accelerating, trying (futilely) to 'outrun' the light, then the observer next to the tracks will also see time slowing down to conserve the speed of light from all perspectives (and from the POV of the guy on the train, the guy next to the tracks get old a lot faster as time appears to speed up).

No matter what you do to try to make light speed appear different to different observers, each observer's measurement of length and/or time will adjust exactly enough to keep the measured light speed constant.

I know. Apparently the math works out such objects cannot obtain c, but I was trying to overlook that lil fact to illustrate the point that c will appear slower despite being the same. Kind of. That's one reason I diverted to scenarios with 1/4c and 1/2c, to eliminate the pain of the lil fact I was trying to ignore.

Consider this:

If an object is moving at 1/4c and emits a light, the light is not traveling at 1.25c
If an object is moving at 1/2c and emits a light, the light is not traveling at 1.5c

In both cases, light is traveling at c. Speaking of it as if c is relative seems misleading when it's a constant. It being constant is crucial. It's a central tenet of relativity. The postulate doesn't assume the very thing the theory shows. It supports the theory. I'm not trying to undermine the theory. I just want an accurate perspective on the postulate.

 

[bilby]

Something just doesn't sit well with me. It seems to me that light has a universal maximum speed just like Einstein said. It's a universal constant, probably due to some causality principle, but my interpretation is unlike others.

If you are standing still and I walk by you at 2MPH and we both cut a light on at precisely the same time shining towards a building, the beams should reach their destination simultaneously despite our difference in speed. If a third person came up in a very fast jet (3000MPH) and all three lights are cut on, then never mind all this observer jazz. Light can only travel so fast. It's universal. It's a universal constant.

The Michaelson-Morley experiment shows that both observers will measure the same value of c for the speed of light.

Yes, it's counterintuitive. That's why so many physicists had such an emotional reaction to the Michaelson-Morley experiment.

Whether or not it makes sense to you is irrelevant. It is true, and it has been verified again and again by experiment.

I'm okay with the counterintuitiveness. I'd like to walk the road of facts whereever it might lead, whether I like it or not, but must I remain silent in the face of curiosity while quips are intimated my way? Surely it can withstand some probing from lil-o me.

I'm not so sure this ACTUAL experiment was designed with my shade of curiosity in mind. Do you not see the ambiguity in "both observers will measure the same value of c for the speed of light?"

If you are traveling at 1/4c, you will measure c as c, and if I am traveling 1/2c, I will measure c as c. Got it.

But, from this, you think what exactly? The bulb on the caboose is traveling at the speed of light, but let's slow it down by 1MPH and cut the light on, the photons emitted will now travel at c, but relative to you, it will take off slower than walking speed relative to the train carrying the bulb. Put the bulb on front of the engine car and bump the speed of the train up 1MPH until it reaches the speed of light. According to some, the light will take off and brighten our way, but my thinking is that relative to me, the light will not shine to light up our way.

The light may appear to move at less than walking speed to an observer standing by the tracks; But it will reach the locomotive at the same time the guy in the caboose thinks it does (even though to him it traveled at light speed), because to the guy standing by the tracks, the train is very, very short - indeed, it is a microscopically thin lamina at c minus 1mph, from his perspective. It gets there at the same time, without going faster, and it does this by not having as far to go.

Light speed is constant for all observers; length and time are variable to allow this. It's counterintuitive, but it's true. A metre is shorter at high speed than it is at rest; an accelerating body ages more slowly than a non-accelerating one. The Apollo astronauts are about 0.25 seconds younger than they would have been if they had stayed at home instead of going to the Moon.

 

[skepticalbip]

I agree, but others do not.

Consider the caboose example in the OP and the responses to it. If the train is traveling at the speed of light, the light on the caboose will not shine and light up the engine train, for the speed of light would have to travel faster than the caboose, and light cannot do that because that would require the speed the light is traveling to exceed c.

The train cannot travel at the speed of light. As an object with non-zero mass approaches light speed, adding more energy to make it go faster contributes to its mass, more than it contributes to its speed. Kinetic energy is proportional both to mass and to the square of velocity, so to add a bit of velocity to an already fast moving object you need to add a lot of energy, which means you also add a lot more mass, and as the velocity approaches light speed, the mass (and hence the extra energy required for further acceleration) approaches infinity. Unless you have infinite energy available, you can't accelerate an object with a non-zero rest-mass to light speed; and an object with zero rest mass (eg a photon) cannot travel at any other speed in a vacuum, because to do so would imply zero energy - and an object with zero energy and zero mass is equal to no object at all. Interestingly, this also means that from a photon's perspective, time doesn't exist - a photon that arises in a quasar at the edge of the observable universe, and that takes millions of years (as measured by us) to reach our telescope, will, from the perspective of the photon, have been emitted by the quasar and absorbed by the telescope's optics simultaneously, having traveled zero distance. To a photon, everywhere is the same place.

If the train is traveling at 99.999% of the speed of light (add any finite number of 9s after the decimal point), then the light on the caboose will travel at the speed of light - as measured by the guy on the caboose - and return to him, lighting up the locomotive; It will be just as if the train wasn't moving at all from his POV.

An observer next to the tracks will see the same thing - but the train will appear to be very much shorter than the guy in the caboose thinks it is, so the light will still travel from one end to the other in the same amount of time, despite only moving fractionally faster than the train itself.

If the train is accelerating, trying (futilely) to 'outrun' the light, then the observer next to the tracks will also see time slowing down to conserve the speed of light from all perspectives (and from the POV of the guy on the train, the guy next to the tracks get old a lot faster as time appears to speed up).

No matter what you do to try to make light speed appear different to different observers, each observer's measurement of length and/or time will adjust exactly enough to keep the measured light speed constant.

I know. Apparently the math works out such objects cannot obtain c, but I was trying to overlook that lil fact to illustrate the point that c will appear slower despite being the same. Kind of. That's one reason I diverted to scenarios with 1/4c and 1/2c, to eliminate the pain of the lil fact I was trying to ignore.

Consider this:

If an object is moving at 1/4c and emits a light, the light is not traveling at 1.25c
If an object is moving at 1/2c and emits a light, the light is not traveling at 1.5c

In both cases, light is traveling at c. Speaking of it as if c is relative seems misleading when it's a constant. It being constant is crucial. It's a central tenet of relativity. The postulate doesn't assume the very thing the theory shows. It supports the theory. I'm not trying to undermine the theory. I just want an accurate perspective on the postulate.

You seem to have reverted to talking about the speed of light without mentioning what that speed is in reference to. Relativity cites what the reference frame is... it is any reference frame in which the measurement is made. In your train thought experiment, that reference frame is the train. For the guy standing by the tracks watching the train speed by, it is his measurement instrument. Both will measure the speed of light (whatever the source) to be the same. This isn't intuitive but is what is actually measured in experiments and what the theory explains.

 

[Kharakov]

"Believers in relativity"?

Seriously?

You would say that bout a scientific fact?

This universe is not the simulation you're looking for.

 

[steve_bank]

As I understand it C is not dependent on an inertial frame.

Throw a baseball forward in a jet cabin and the velocity relative to the ground is the speed of the jet plus the speed of the ball.



Emit a laser pulse from a jet, on the ground the velocity is C.

Two spaceships at rest synch clocks. One accelerates away. On each ship a second is still a second. Nothing appears tp change in the two frames to observers in the frames.

Relativity is consistent and predictive, but to me we are missing something fundamental not that I have a clue what.