I Speed of Light & Bullet

[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.

 

[FRANKENSTEIN54]

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

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



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

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

Maybe I'm not being clear enough . Let's see if we can simplify it .
I'm at rest Relative to a Source object . The object shoots a bullet directly towards Me .
I measure the speed of the bullet from one position in its path at a certain Time , and its position at a later Time , all Relative to Me . Giving Me a Distance travelled in Time . Let's say its travelling a constant 600mph towards Me . So its speed is 600mph Relative to Me , coming directly towards Me .
Let's agree that's all correct . Now let's say I am now moving at a constant speed of 200mph directly towards the bullet . I calculated my speed Relative to the Source object of the bullet. I measure the speed of the bullet Relative to Me to be 800mph . Is that correct ?
I calculate that by adding My speed to its speed . I can calculate the speed of the bullet , while I'm moving , exactly the same way as I calculated it while I was at rest with the Source object of the bullet .
I can calculate my speed as being 200mph while simultaneously calculating the bullet's speed as being 600mph .
I suppose I can also calculate the Relative speed of the bullet towards Me , while I'm also moving towards it , in another way ! By calculating the DECREASE in Distance between Me & the bullet over a certain length of Time . That would work right ? And be simpler . Not sure off-hand , of the Equation for that .

Now let's try it with light , a photon from a source object .

I'm at rest Relative to a Source object . The object emits a photon directly towards Me .
Since I'm lazy now . I'm at Rest !!!!
Just Repeat what I did above , substituting the photon for the bullet , and substituting the speed of light "c" for the speed of the bullet !!!

The speed of the bullet Relative to the source never changed , yet its speed relative to Me Moving increased .
The speed of the photon Relative to the source never changes , is always "c" .
So , why wouldn't I "MEASURE" , as in Calculate the "Relative to Me" speed of the photon to be c + my speed of 200 mph ??
Not saying that the speed of the photon has actually increased !
I guess what I could say is , just using Calculations , "on paper " so to speak , Mathematically , using Positions in Space and using Time , you can use a "Mathematical speed of light" that's greater than "c" .
Just in order to make "on paper" mathematical Calculations that give mathematically correct results !!
And would be fit to describe some aspect of the Physical phenomena , as to what's relative & meaningful to what you want to calculate .
As long as the "Math" is correct , and can apply to all such physical "encounters" , and relied upon to give accurate results that you're actually seeking or want to know .
After all , Einstein himself , in his famous Equation >>> E=Mc2 , uses the "speed of light Squared" !!!???
Now , that's WAY Faster than the speed of light "c" !!!!!!!!!!

 

[Ibix]

I measure the speed of the bullet Relative to Me to be 800mph . Is that correct ?

No, it is wrong. See post #57 for the correct calculation and the explanation of why simply adding low velocities almost works, and post #58 for a worked example.

The correct answer, given your 600mph and 200mph figures, is 799.9999999998mph. Your mistake amounts to around 0.3 microns per hour at these speeds, which is utterly negligible. But your error gets larger and larger as either velocity approaches $c$.

 

[PeroK]

After all , Einstein himself , in his famous Equation >>> E=Mc2 , uses the "speed of light Squared" !!!???
Now , that's WAY Faster than the speed of light "c" !!!!!!!!!!

If Einstein was wrong about relativity in the first place, then why would you trust $E = mc^2$? That makes no sense. My last thought on this is to refer you to Dunning and Kruger:

https://en.wikipedia.org/wiki/Dunning–Kruger_effect

 

[Nugatory]

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

No, of course not. Clocks work just fine.

However, your post #70 makes it clear that you haven’t been paying any attention to the answers you’re getting here - compare what you said in #70 with what we’ve already said in 23, 27, 29, 57, 58, 63. This is just wasting your time and ours so the thread is closed.

If you want to understand this part of how the world works, you should start with a proper textbook - many recommendations in this forum already. We can help you over the hard spots if you’re making a good faith effort to learn, but what what you’re doing in this thread isn’t that.