A well defined thought experiment

[Ibix]

They don't agree on the elapsed time. They do agree on the distance travelled by the lift or light pulse. Therefore they don't agree about the speed.

I don't understand why this is difficult.

 

[PeterDonis]

I would think that both Alice and Bob measure the height of buildings the same, i.e. 1000 meters.

Yes.

It is therefore ruled out that d (distance) the photon travels up and down is different for Alice and Tom, - right ?

For the case where the photon travels purely vertically, yes.

The speed of the photon is not affected by both Bob and Alice watching it move (up and down) for 100 billion years.

Not by that, but it is different for Alice and Bob because their relative clock rates are different. That means the speed of the photon is different for each of them.

Bob and Alice must (off course) also agree on how many times the photon has traveled up and down. (?)

Yes.

When we assume that Bob and Alice receive a light signal every time the photon hits the bottom and top of the skyscraper, they both just have to count these signals and multiply by distances of 1000 meters (which is the height of the skyscraper) - then they both have to be 100% sure of how far the photon is have traveled.

Yes, they agree on the distance the photon traveled. But they do not agree on the time it took to travel; that time is different for each of their clocks.

when Bob and Alice now calculate the distance that the photon has traveled, based on the time shown by their clocks, - they will not agree.

Yes, they will, because unlike you, they will not be using the same speed of light. This point has already been made in previous posts.

Should the mystery lie in the fact that Bob and Alice do not perceive the speed of light the same (?)

Yes, as has already been said in previous posts, as well as above.

In that case, let's say that Bob and Alice have also measured how many times the elevator has gone up and down.

After all, Bob and Alice can only agree that the elevator has run up and down 8.64e15 times
When Bob and Alice calculate 8.64e15 * 1000 meters, they both agree and get the same result (8.64e18 meters).

Yes, but they will disagree on the time it took the elevator to do that, so they will disagree on the elevator's speed.

Let's say the elevator speed is 500m/s

We can't, because the elevator speed is not the same for Alice and Bob.

Alice claims that when she calculates the distance the elevator has traveled based on the time she has measured, the result is :(3153.6 seconds * 500m/s) = 1576800 meters less than the travel distance that Bob has calculated based on the time Bob has measured..

No, she doesn't, because, once again, unlike you, she understands that the speed of the elevator is different for her than it is for Bob.

It is then a paradox that Bob and Alice again first agree and then disagree (?)

No, because they don't. They always agree on the number of transits and the distance, and they always disagree on the elapsed time.

I'm sorry, but I have a hard time understanding where the solution to this dilemma is?

That's because you have ignored the statements already made in previous posts (which I have repeated above) about the speeds being different. You need to stop doing that. You can't possibly get the right answer if you ignore it when it's put right in front of your face.

 

[PeterDonis]

Bob and Alice also calculated the distance the elevator was travelling up and down, first they agreed,on calculation and right after they disagree, read my post above, so it cannot be limited to be a speed of light problem

Wrong. See post #32.

 

[Mikael17]

They don't agree on the elapsed time. They do agree on the distance travelled by the lift or light pulse. Therefore they don't agree about the speed.

I don't understand why this is difficult.

I can easily understand that. But the question is which parameter is what changes in a gravitational field if you compare Bob's and Alice's reality. We know that Alice's clock ticks slowing . We know d is the same, - The only possibility is therefore purely mathematical that m (the ruler) must also be a relative variable?

 

[Ibix]

But the question is which parameter is what changes in a gravitational field if you compare Bob's and Alice's reality.

The elapsed times. You just agreed that!

 

[PeterDonis]

which parameter is what changes in a gravitational field if you compare Bob's and Alice's reality

We're not comparing their "realities". They both live in the same reality. In that one reality, the length of the paths that Alice and Bob take through spacetime are different; that is what "different elapsed times" means.

We know that Alice's clock ticks slowing . We know d is the same,

Yes, good, you've got it. Except--

The only possibility is therefore purely mathematical that m (the ruler) must also be a relative variable?

No, the "only possibility" is that Alice's clock runs slow, just as you already said in the quote above.

 

[PeroK]

Bob and Alice also calculated the distance the elevator was travelling up and down, first they agreed,on calculation and right after they disagree, read my post above, so it cannot be limited to be a speed of light problem

I've read your posts and I don't understand the problem. We are talking about observers at two locations above the surface of the Earth. For precise measurements, you want to take the curved spacetime around the Earth into account. The geometry of this spacetime can be described in Schwarzschild coordinates. You're starting point is, therefore, a mathematically well-defined description of this region of spacetime. Where's thr problem?

You might be interested in the Pound-Rebka experiment.

https://en.wikipedia.org/wiki/Pound–Rebka_experiment

 

[Dale]

I would think that both Alice and Bob measure the height of buildings the same, i.e. 1000 meters.

This claim requires a bit of clarification. What method are they using to measure the height? Using radar they will agree that the speed of light in the vertical direction is $c$, but disagree on the height. Using the same ruler they will agree on the height but disagree on the speed of light. Using a difference in coordinates will depend on whether or not they are using the same coordinates.

Both bob and Alice are therefore both calculated that the photon has traveled (94608000000000000000000 * 1000 meters).

Wait. I thought the light pulse was bouncing back and forth horizontally, not vertically. Please clarify.

Should the mystery lie in the fact that Bob and Alice do not perceive the speed of light the same (?)

Sloppy descriptions are not the same as mysteries.

Let's say the elevator speed is 500m/s

If they disagree on the speed of light, do you think they will agree on the elevator speed?

I'm sorry, but I have a hard time understanding where the solution to this dilemma is?

Part of the reason that you are having a hard time is that you are jumping around in your analysis. You are making unjustified assertions and using those in a haphazard manner. You are trying to construct a mental model patched together with guesswork and finding that it is shaky. That doesn’t mean that there is not a solid model available, just that what you are doing is not it.

 

[PeterDonis]

I thought the light pulse was bouncing back and forth horizontally, not vertically.

The OP has described two scenarios in the thread; the original one with horizontally bouncing light, and a later one with vertically bouncing light. He's making the same error in both of them.

 

[Mikael17]

That's because you have ignored the statements already made in previous posts (which I have repeated above) about the speeds being different. You need to stop doing that. You can't possibly get the right answer if you ignore it when it's put right in front of your face.

I'm sorry, but I'm still confused
What you actually write here is that: - both the photon + the mouse are both "schizophrenic".

Neither the mouse nor the photon can travel at two speeds simultaneously (depending on who is observing them).
As I see it: The only way to express the answer to my question must be that Alice and Bob do not perceive the speed in the same way.
It is a completely different story - than claiming that speed is different.

The only way to express this mathematically is: The perception of speed is different.

Speed is by definition meter (m) / per second (s) = (d) - distant.
Bob and Alice agree about d (distance) to be the same.
Bob and Alice agree about measured t (is different for Alice and Bob)

The only parameter that remains is therefore m (the ruler)

Bob and Alice must also agree that they must have different perception of the length of the same meter ruler, depending on whether the ruler is at Alice's apartment or at Bob's apartment.
This is my point.

Its is in fact very different to make any other logical sense of this
If this is still false please tell me where the chain went off?

 

[PeroK]

Neither the mouse nor the photon can travel at two speeds simultaneously (depending on who is observing them).

Speed is, and always has been, a frame dependent quantity. In SR, the speed of light is frame invariant (across inertial reference frames). In GR, SR applies locally and the locally measured speed of light is always $c$. But, in GR, the coordinate speed of light is not necessarily $c$. There are no global inertial reference frames in GR.

 

[Mikael17]

Speed is, and always has been, a frame dependent quantity. In SR, the speed of light is frame invariant (across inertial reference frames). In GR, SR applies locally and the locally measured speed of light is always $c$. But, in GR, the coordinate speed of light is not necessarily $c$. There are no global inertial reference frames in GR.

This is not only about the photon but also about the mouse.
You did not answer my question.
How can Alice and Bob logically and mathematically understand what happens in there own apartments. (or in other apartments in the same building)

Do you agree that Bob and Alice have different perception on speed, and that this is what this discussion is really about, - (or should be about)?
And do you agree that in the end of the day that means Bob and Alice have different perception of the ruler.

 

[PeroK]

This is not only about the photon but also about the mouse.
You did not answer my question.
How can Alice and Bob can logically and mathematically understand what happens in there own apartments.

Do you agree that Bob and Alice have different perception on speed, and that this is what this discussion is really about, - (or should be about)?
And do you agree that in the end of the day that means Bob and Alice have different perception of the ruler.

If you want to learn physics, then I'm happy to help. These questions make too little sense for me to be interested in answering them. For example, "perception" is not a word I would use in connection with physics.

I'd also say that GR (curved spacetime) is a conceptual challenge even for a well-prepared physics student. Given your approach and attitude towards it, I'd say you are being sucked into a black hole of confusion and misunderstanding.

 

[Ibix]

Neither the mouse nor the photon can travel at two speeds simultaneously (depending on who is observing them).

Sit in a chair in a train with a coffee on a table in front of you. How fast is your coffee travelling according to you? How fast is it travelling according to someone standing on an embankment watching the train pass?

Things moving at different speeds depending on who is doing the measurement are utterly commonplace. Curved spacetime just affords new opportunities to make different measurements of the same thing.

Speed is by definition meter (m) / per second (s) = (d) - distant.
Bob and Alice agree about d (distance) to be the same.
Bob and Alice agree about measured t (is different for Alice and Bob)

Just stop here. Alice and Bob measure the same distance but different times. Therefore they measure different speeds. Either can use gravitational time dilation to deduce the time and hence the speed that the other measures. No more explanation is needed.

 

[Ibix]

Alice and Bob measure the same distance but different times. Therefore they measure different speeds.

Note that this is the reverse of the Newtonian case. With the coffee on the train and a Newtonian analysis, you and the person on the embankment would agree on the time between ticks of your clocks, but not the distance travelled by the coffee.

 

[Mikael17]

If you want to learn physics, then I'm happy to help. These questions make too little sense for me to be interested in answering them.

Thank you

For example, "perception" is not a word I would use in connection with physics.

Very sorry to hear that, as I understand Einstein explained a lot that depended on how different observers perceive something that happens in other frames of reference and the consequences of that.

I'd also say that GR (curved spacetime) is a conceptual challenge even for a well-prepared physics student. Given your approach and attitude towards it, I'd say you are being sucked into a black hole of confusion and misunderstanding.

´That is why we use the elevator as an example, which should eliminate a lot of confusion

 

[Mikael17]

Therefore they measure different speeds.

I understand what you wrote, I also understand that the concept of "speed" then "must" have a stange schizophrenic or multi-schizophrenic nature depending on who and how many observers in different gravity levels measure this speed. - But that does not mean that it is easy to accept, nor that I can accept it.

 

[Ibix]

Very sorry to hear that, as I understand Einstein explained a lot that depended on how different observers perceive something that happens in other frames of reference and the consequences of that.

I would say you understand wrong. "Perceive" is a rabbit hole of subjective judgements - a lecture can be perceived to flow by quickly if you find it interesting or drag on forever if you don't. Objective measurement, on the other hand, will show that it lasts the same either way. The altitude or state of motion of the clock used affects the measured duration, not your perception.

Einstein talked a lot about operational definitions of things - measurement based definitions. Not perceptions. I think this is part of your problem here. You seem to accept that Alice and Bob mke different measurements of the same thing, but you then get hung up on some imagined process after them dividing one number by the other. Stop inventing extra steps.

 

[PeroK]

But that does not mean that it is easy to accept, nor that I can accept it.

That makes no difference to anything. Science goes on regardless of whether you like it or not!

 

[Ibix]

But that does not mean that it is easy to accept,

Welcome to relativity.

The journey is (a) understanding that you have an intuitive physical model that matches well with Newtonian physics, (b) understanding that this model is not accurate outside a narrow range of circumstances, and (c) developing a more general mental model. Learning the maths is pretty much required for going from (b) to (c), and is conceptually challenging even with the maths.

 

[Mikael17]

You seem to accept that Alice and Bob mke different measurements of the same thing, but you then get hung up on some imagined process after them dividing one number by the other. Stop inventing extra steps.

I consider d = t * v mathematically, and that v= m (meter) per s (second) .
I realized that t is variable, and I understand that when v is not equal, for Alice and Bob, - then mathematical consequence, can only be that m is not equal either. Sorry this is not my "invention" this i math.

 

[Ibix]

also understand that the concept of "speed" then "must" have a stange schizophrenic or multi-schizophrenic nature

The thing is, this bit is totally mundane. Your speed if you are sitting in your chair is zero. Or it's several hundred miles per hour (the Earth surface rotation speed at your latitude) if you take the Earth's rest frame. Or it's about twenty kilometres per second (Earth's orbital speed) if you take the Sun's rest frame. That's just a consequence of different definitions of "at rest".

A lot of students do struggle with this notion, but it underlies Newtonian physics too - which suggests a review of classical kinematics is probably necessary before you even try Einstein's relativity.

Sorry this is not my "invention" this i math.

It is completely your invention.

Speed is literally the answer to "how many meters did this thing travel in one second". If Alice and Bob agree on the distance travelled but not the time taken then they disagree on the number of meters travelled in one second. That's it. There's no need to redefine the meter. In your scenario they can even both use the same meter rule to measure the distance travelled, in which case they can't possibly be using a different definition.

 

[Motore]

I consider d = t * v mathematically, and that v= m (meter) per s (second) .
I realized that t is variable, and I understand that when v is not equal, for Alice and Bob, - then mathematical consequence, can only be that m is not equal either. Sorry this is not my "invention" this i math.

d = 1000m, tA = 10s, tB = 5s
vA = d/tA = 1000m/10s = 100m/s
vB = d/tB = 1000m/5s = 200m/s
So the distance is the same, the speeds and times measured by Alice and Bob are not.
What is bothering you exactly?

 

[Dale]

the concept of "speed" then "must" have a stange schizophrenic or multi-schizophrenic nature depending on who and how many observers in different gravity levels measure this speed

This is unacceptable language for this forum. Nowhere in any professional scientific literature is speed described as schizophrenic. This is untrue and pejorative, and it trivializes a severe mental illness.

Furthermore, this is standard fare for ordinary Newtonian physics. Speed has always been frame variant (the correct term). Even in normal Newtonian physics the speed of a person walking in the aisle of a bus is maybe 1 kph relative to the bus and 101 kph relative to the ground. So your objection is not specifically relativistic.

Frame variant things are frame variant. Not schizophrenic. And the list of what things are frame variant differs between relativity and Newtonian physics, but the idea of frame variance is a standard and you cannot do even classical physics without it. You need to accept that idea if you wish to learn physics.

I realized that t is variable, and I understand that when v is not equal, for Alice and Bob, - then mathematical consequence, can only be that m is not equal either. Sorry this is not my "invention" this i math.

This is illogical. If the difference in $t$ explains the difference in $v$ then there is no need to additionally posit some weird variation in $m$. Furthermore, physics can be done in other units besides SI units. So positing some weird variation in $m$ wouldn’t resolve the issue anyway.

 

[PeterDonis]

Neither the mouse nor the photon can travel at two speeds simultaneously (depending on who is observing them).

Yes, they can. Speed in relativity is observer dependent.

I understand Einstein explained a lot that depended on how different observers perceive something that happens in other frames of reference and the consequences of that.

Einstein may have used the term "perceive" (his original writings are in German so we'd have to look at the German word he used), but if he did, he did not mean by it what you mean by it. The observer-dependent speeds in relativity are not subjective perceptions but objective measurements; different observers make different objective measurements that are the "speed" according to them.

You have been given the correct answer multiple times now in this thread, by multiple experts on the subject. If you don't want to accept it, we can't help you any further. Thread closed.

 

[Dale]

As an appendix, if we start with the usual Schwarzschild line element $$ds^2=-\left(1-\frac{R}{r}\right)dt^2 +\left(1-\frac{R}{r}\right)^{-1}dr^2+ r^2d\theta ^2+ r^2 \sin ^2(\theta )d\phi ^2$$ And we define the perspective of an observer hovering at $r_0$ to be given by the transformation $$t \rightarrow \left( 1-\frac{R}{r_0} \right)^{-1/2} T$$ Then for the vertical light pulse we can set $d\theta=d\phi=0$ and $ds^2=0$ and solve for $dr/dT$ to get the coordinate speed of light in the radial direction for a given observer which is $$\frac{dr}{dT}\bigg|_{\text{radial light}}=\left(1-\frac{R}{r} \right) \left( 1-\frac{R}{r_0}\right)^{-1/2}$$ Note that this depends on $r_0$, so different observers hovering at different radii will disagree about the speed of light, as mentioned above many times. This fully accounts for all of the disagreements between Alice and Bob. There is nothing left over to explain. I leave it as an exercise to the interested reader to show that this definition of the perspective of a hovering observer will agree on spatial distances.