Speed of Light & Bullet

[Sagittarius A-Star]

When AE says of the two lightening strikes that there can be no simultaneity of relativity between the moving and stationary observers because of additive result of C plus the train’s speed, would that be suggesting that information can be transmitted or translated across a distance faster than C?

No. The light moves with speed $c$ with reference to the rest-frame of the embankment, even if the closing speed $c + v$ between the train and the light from event $B$ (with reference to the rest-frame of the embankment) is greater than $c$.

The light moves also with speed $c$ with reference to the rest-frame of the train.
In Einsteins thought experiment, the observer in the train does not see the flashes simultaneously because they do not happen simultaneously with reference to the rest-frame of the train and he is located equidistant to the train-locations, where the events happened.

Source:
https://en.wikisource.org/wiki/Relativity_(1931)/Section_9

 

[Dale]

the unchanged speed of light for all observers mean that a ship passing earth at time “0” and a uniform .2 C toward the sun, does not observe the sunspot appear or the solar flare, before earth receives that information?

Such an observer would receive the information before the earth does in all frames.

 

[davidjoe]

Such an observer would receive the information before the earth does in all frames.

Seems very logical, but if the direction of relativistic travel can cause events on the sun in front of the ship to appear to unfold sooner and more rapidly, to the astronauts, then what would the affect be viewing events to the sides and rear of the ship?

 

[Dale]

See relativistic aberration:
https://en.wikipedia.org/wiki/Relativistic_aberration

Or relativity of simultaneity:
https://en.wikipedia.org/wiki/Relativity_of_simultaneity

Depending on if you are talking about actually what you visually see or what you calculate after accounting for light travel delays.

 

[FRANKENSTEIN54]

That's one of the things you learn when you study physics. Things that make sense aren't always true, and things that are true don't always make sense.

You have a fundamental misunderstanding of natural science in general and physics in particular. Physics is a study of phenomena. Often it provides an explanation or description. That explanation or description may or may not make sense to you, but that doesn't matter. All that matters is that the description matches observation.

In the case you are discussing it just so happens that it does make sense. You just have to study it further. The idea has been around for almost 120 years. It made sense then and it still makes sense now.

If you could devise a bullet that traveled at speed $c$ all observers, regardless of their speed relative to each other, would observe its speed to be $c$. It makes perfect sense to me, lots of other people; and more importantly to the thousands of technicians, engineers, and scientists working in hundreds of places across the globe it is an everyday fact of life.

That's what I mean by "making sense" though . As you say , Physics can explain or describe something which "matches" observation . If it matches observation , then I would say it "makes sense" . Why would the bullet have to move at speed c , before all observers , regardless of their speed relative to each other , would observe/measure its speed to be c ?

 

[FRANKENSTEIN54]

A few question for you which may be helpful in your thinking, and will at least be helpful in clarifying your posts. Sitting in your chair, right now at your computer, what is your "speed through space" you talk about?

To anticipate, you might say it is zero, which is what I would probably say about myself if someone asked me what my speed was right now. But then, what about the Earth orbiting the sun. If my "speed through space" is zero, and the ground is moving at the same speed I am, then the ground - the Earth - must also have a speed through space of zero. We can explore the consequences of that if that's the route you're taking, I suppose, but it's got some issues with the Copernican model of the solar system among other issues.

On a historical note, this sort of thing was talked about by Galielo in the context of the Copernican model of the solar system. At t his point, it's got nothing to do with special relativity, it's purely about Newtonian mechanics. A key buzzword: "Galilean relativity".

But, perhaps, you will answer that your speed through space is not zero. I can't tell, unless you answer the question. Then what would you say this speed is? And how do you know? Is there some way of measuring it?

I should add for clarity that I do not agree that there is such a thing as a "speed through space", but I think the best chance of any sort of discussion is to ask you some questions rather than write some lecture.

Well , all speed is relative to some point in space/time . An object moving from point A in space to point B in space , would have a "speed through space" .

 

[PeroK]

Well , all speed is relative to some point in space/time . An object moving from point A in space to point B in space , would have a "speed through space" .

What's your current speed through space? And, more important, how would you measure it?

 

[Ibix]

Why would the bullet have to move at speed c , before all observers , regardless of their speed relative to each other , would observe/measure its speed to be c ?

It's a postulate of relativity that the speed of light is invariant. We accept that this is correct because there is a huge amount of evidence that it is so. Why it should be so, though, we do not know.

Well , all speed is relative to some point in space/time . An object moving from point A in space to point B in space , would have a "speed through space" .

How are you defining a "point in space"? You can't make a scratch on space to mark it.

If you work through that chain of thought you get to where Galileo got to in the 1600s, that there is no absolute meaning of "at rest". And hence, there is no meaning to "speed" except relative to a physical object.

 

[FRANKENSTEIN54]

The equation for the relative speed of a bullet and light are identical, but the numbers and velocity are extremely different. The bullet relative speed is very slow compared to light but it is not exactly the simple addition of speeds. The difference is so small that nobody would notice. By the time you get close to light speed, the correct equations are so different from simple addition of speeds that it is impossible to ignore. And by the time you get to the speed of light, "c", it has reached the limit and any change of the observer speed makes no difference at all.

Can't you measure an objects location in space at one Time , to its next location after x amount of time ?? So you're measuring it Relative to its original location , and basically irrelevant to your location or motion after x amount of time . As you say , bullet relative speed is very slow compared to light . So yes , slow movements towards bullet " add up" . But since light already travels really fast , then "slow" movements towards light would also be a difference so small that "nobody would notice" as you said concerning "simple addition of speeds" . I guess what I'm getting at is , it seems people ADD their speed towards the bullet to arrive at the "Relative speed" of the bullet ! Which is fine . But they DON'T ADD their speed towards the Light to arrive at the "Relative speed" of Light !???? So , which is it ? The bullet & the light are still moving at an "absolute" constant speed towards you , at a rate measured if you were Not moving towards them .

 

[Ibix]

Can't you measure an objects location in space at one Time ,

No, you can't (not without defining a state of rest first, which is a free choice). Thinking you can is where you go wrong.

 

[PeroK]

Can't you measure an objects location in space at one Time , to its next location after x amount of time ??

Yes, and that means you would measure your own speed through space as zero. But, not every observer would measure that. That's only relative to your chair, room and the surface of the Earth below you.

 

[FRANKENSTEIN54]

No, you can't. Thinking you can is where you go wrong.

What ??? So how can you measure anything if you can't determine where an object is ???

 

[PeroK]

What ??? So how can you measure anything if you can't determine where an object is ???

You can determine where it is relative to you!

 

[FRANKENSTEIN54]

You can determine where it is relative to you!

Well of course , everything is in relation / Relative to the Observer .

 

[Ibix]

What ??? So how can you measure anything if you can't determine where an object is ???

You can use a ruler. But you picked the ruler to be at rest when you did.

How were you planning on recording where something was without using a ruler, or a radar set or something? That's the question you need to answer.

 

[PeroK]

Well of course , everything is in relation / Relative to the Observer .

Including velocity/speed.

 

[Ibix]

Well of course , everything is in relation / Relative to the Observer .

...and not relative to "space". So you agree that you are not measuring "speed through space", you are measuring speed relative to something?

 

[FRANKENSTEIN54]

You can use a ruler. But you picked the ruler to be at rest when you did.

How were you planning on recording where something was without using a ruler, or a radar set or something? That's the question you need to answer.

Well , all Measurements are done in an instant of Time . So everything is virtually "at rest" / "frozen in time" at the moment of measurement .

 

[PeroK]

Well , all Measurements are done in an instant of Time . So everything is virtually "at rest" / "frozen in time" at the moment of measurement .

If the object is somewhere else at a later time, then it has a non-zero average velocity in your frame of reference. That's the definition of velocity, which by definition is relative to some reference frame or observer.

For example, in a game of tennis, the speed of each serve is measured and shown on the scoreboard. But, that's the speed of the ball relative to the court. If you really believe in one, absolute speed that everyone measures, then the speed shown on the scoreboard should at least include the speed of rotation of the Earth's surface and probably the speed of the Earth's orbit round the Sun. The scoreboard should say that the speed of the serve is about 200,000 km/h.

And this example shows precisely why an absolute speed "through space" that everyone measures cannot be defined.

 

[Orodruin]

It may help to some extent to remove the ground, which most people would intuitively take as being at zero velocity (it is the implicit assumption in laws regarding speed limits on roads etc).

Think anout two rockets in space that are only cruising at some fixed velocity relative to eachother. Which one is at rest? How would the astronauts determine which is at rest?

(The answer is that they cannot determine who is at rest. Any experimemt performed by one will have the exact same outcome if performed by the other.)

 

[Ibix]

Well , all Measurements are done in an instant of Time . So everything is virtually "at rest" / "frozen in time" at the moment of measurement .

Can't you measure an objects location in space at one Time , to its next location after x amount of time ??

You seem to be confusing yourself. You are explicitly using a measurement over time here, as you must, but denying that it's a measurement because it isn't at an instant (?).

The point, of course, is that you have to take account of how the ruler moves between the two position measurements. You have to assume a state of motion for the ruler, which is where you bring in your assumption of the state of rest.

 

[Orodruin]

I guess what I'm getting at is , it seems people ADD their speed towards the bullet to arrive at the "Relative speed" of the bullet ! Which is fine . But they DON'T ADD their speed towards the Light to arrive at the "Relative speed" of Light !???? So , which is it ?

Both. As has already been mentioned in this thread, velocities never simply add. They have to be composed using the relativistic formula for velocity addition:
$$
v’ = \frac{v+u}{1+uv/c^2}
$$
For $u$ and $v$ both much smaller than $c$, this is well approximated by $v’ = u+v$. That’s the case of the bullet. We can add small velocities because the correction to that addition are vanishingly small and typically will be within measurement errors. However, for $v=c$ the result is always $v’=c$.

 

[Ibix]

We can add small velocities because the correction to that addition are vanishingly small and typically will be within measurement errors. However, for $v=c$ the result is always $v’=c$.

Worked example: 70mph is approximately 30m/s, or $10^{-7}c$. Two cars heading towards each other and each travelling at 70mph relative to the ground, then, do not see each other closing at 140mph, but at 139.9999999999996mph (if I've counted the nines correctly). That is, as Orodruin said, a far smaller error than could be measured, which is why just adding velocities works at low speeds.

 

[jbriggs444]

Well , all Measurements are done in an instant of Time

According to the theory of special relativity, the notion of an "instant in time" is less absolute than one might suppose. One does not have an arbitrary "moment in time". Instead, one has an arbitrary hyper-plane of simultaneity.

Inertial frames in relative motion will disagree about simultaneity. This profoundly affects their measurements of speed.

 

[Dale]

If it matches observation , then I would say it "makes sense"

By that definition relativity makes sense. See here for a summary of many of the observations it matches:

https://math.ucr.edu/home/baez/physics/Relativity/SR/experiments.html

 

[FactChecker]

Can't you measure an objects location in space at one Time , to its next location after x amount of time ??

Any inertial reference frame can measure these in its coordinate time and space. Other inertial reference frames will disagree.

So you're measuring it Relative to its original location , and basically irrelevant to your location or motion after x amount of time . As you say , bullet relative speed is very slow compared to light . So yes , slow movements towards bullet " add up" .

Only if you are willing to ignore the tiny disagreements that different inertial reference frames would have.

But since light already travels really fast , then "slow" movements towards light would also be a difference so small that "nobody would notice" as you said concerning "simple addition of speeds" . I guess what I'm getting at is , it seems people ADD their speed towards the bullet to arrive at the "Relative speed" of the bullet ! Which is fine .

But they DON'T ADD their speed towards the Light to arrive at the "Relative speed" of Light !????

Light already travels at the maximum speed that exists in the geometry of SR spacetime. You can not add any speed to it.

So , which is it ? The bullet & the light are still moving at an "absolute" constant speed towards you

Nothing is "absolute" in measuring velocity. All times and distances depend on what inertial reference frame is being used.

 

[Orodruin]

According to the theory of special relativity, the notion of an "instant in time" is less absolute than one might suppose. One does not have an arbitrary "moment in time". Instead, one has an arbitrary hyper-plane of simultaneity.

If only a long-time appreciated member of PF would put something about this in their signature so we didn’t have to repeat it over and over!

 

[Dale]

Why would the bullet have to move at speed c , before all observers , regardless of their speed relative to each other , would observe/measure its speed to be c ?

If you work through the math you find that there can be only one invariant speed, c. So going c with respect to one observer is the same as going at c with respect to any and all observers.

Well , all speed is relative to some point in space/time . An object moving from point A in space to point B in space , would have a "speed through space" .

Note that picking a “point A in space” involves more than identifying a single point out of a 3D space. You have to identify that point at each moment in time, and do so in a continuous fashion. So point A in space is a location at each point in time. That gives A a four-velocity, and recall that speed requires two four-velocities. So yes, it is sufficient to identify a point A, but it actually gives more structure than what is needed.

I guess what I'm getting at is , it seems people ADD their speed towards the bullet to arrive at the "Relative speed" of the bullet ! Which is fine . But they DON'T ADD their speed towards the Light to arrive at the "Relative speed" of Light !???? So , which is it ?

For both light and bullets at any speed you use the relativistic velocity addition formula. The rule is the same for every object, it is just different from the Newtonian approach.

https://en.m.wikipedia.org/wiki/Velocity-addition_formula

The bullet & the light are still moving at an "absolute" constant speed towards you

This is not correct and you are already aware of this. Please do not continue to repeat it.

 

[weirdoguy]

If only a long-time appreciated member of PF would put something about this in their signature so we didn’t have to repeat it over and over!

I don't know how other people see this, but on my computer it's not that visible:

It becomes more visible when you put a cursor on it. Anyways, as a person whose sight is not very good, and I refuse to wear glasses, I kind of understand a lot of people do not see it

 

[FRANKENSTEIN54]

If you work through the math you find that there can be only one invariant speed, c. So going c with respect to one observer is the same as going at c with respect to any and all observers.

Note that picking a “point A in space” involves more than identifying a single point out of a 3D space. You have to identify that point at each moment in time, and do so in a continuous fashion. So point A in space is a location at each point in time. That gives A a four-velocity, and recall that speed requires two four-velocities. So yes, it is sufficient to identify a point A, but it actually gives more structure than what is needed.

For both light and bullets at any speed you use the relativistic velocity addition formula. The rule is the same for every object, it is just different from the Newtonian approach.

https://en.m.wikipedia.org/wiki/Velocity-addition_formula

This is not correct and you are already aware of this. Please do not continue to repeat it.

If you are at rest Relative to the source that fires a bullet directly towards you , and it attains a constant speed of 600 mph towards you while you remain at rest . If you then move directly towards the bullet , does the bullet itself then gain speed relative to its source ? I think not . Relative to you moving towards the bullet , then I guess you can say it's speed Relative to you is faster than 600 mph . 600 + your speed .
You only get / calculate that relative speed because you ADD your speed to its speed .
When Light is travelling directly towards you , why don't you ADD your speed towards the light , to the speed of light , to calculate the Relative speed of the light towards you ??? Resulting in c + your speed , as the Relative speed of light towards you ??? Why change the Mathematical equation for determining Relative speed of the bullet from the light ? Isn't Speed calculated by Distance of object travelled per Time elapsed ?

 

[FRANKENSTEIN54]

If only a long-time appreciated member of PF would put something about this in their signature so we didn’t have to repeat it over and over!

So , throw all Clocks out the window into the " hyper plane of simultaneity" ???

 

[Ibix]

When Light is travelling directly towards you , why don't you ADD your speed towards the light , to the speed of light , to calculate the Relative speed of the light towards you ???

Because you don't add velocities ever. See post #57.

 

[PeroK]

If you are at rest Relative to the source that fires a bullet directly towards you , and it attains a constant speed of 600 mph towards you while you remain at rest . If you then move directly towards the bullet , does the bullet itself then gain speed relative to its source ? I think not . Relative to you moving towards the bullet , then I guess you can say it's speed Relative to you is faster than 600 mph . 600 + your speed .
You only get / calculate that relative speed because you ADD your speed to its speed .
When Light is travelling directly towards you , why don't you ADD your speed towards the light , to the speed of light , to calculate the Relative speed of the light towards you ??? Resulting in c + your speed , as the Relative speed of light towards you ??? Why change the Mathematical equation for determining Relative speed of the bullet from the light ? Isn't Speed calculated by Distance of object travelled per Time elapsed ?

There are several assumptions there that you don't notice you are making - because they seem so obvious to you. To be fair, that's what everyone thought must be case until 1905, when Einstein published the paper on SR. In fact, the introduction to the 1905 paper goes into detail to explain all the assumptions you are making about space, time and measurements of distance and time. And why something important is being missed.

The short answer is that you are assuming a Newtonian universe without realising that assumption may not be true. Moreover, many experiments have shown your assumptions to be false.

Also, this is post #67 and you are still trying to convince us that all of modern physics (since 1905) is wrong and you are right. That's an impossible argument, because modern physics is backed up by a mountain of experimental evidence. If you don't want to accept that physics has progressed beyond what seems obvious to you, then there is nothing we can do to change your mind.

 

[Orodruin]

When Light is travelling directly towards you , why don't you ADD your speed towards the light , to the speed of light , to calculate the Relative speed of the light towards you ??? Resulting in c + your speed , as the Relative speed of light towards you ???

This has literally already been addressed in posts 23, 27, 29, 57, 58, 63. If you do not read the replies and reflect on them then there is not much we can do for you.

Why change the Mathematical equation for determining Relative speed of the bullet from the light ?

It didn’t change, as already pointed out in the above posts. It is just that ignoring the denominator in the formula is a good approximation for velocities significantly lower than c.

Isn't Speed calculated by Distance of object travelled per Time elapsed ?

Yes. But neither time nor distance are the same for different observers.