# A problem to the theory of relativity ?

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A thought experiment

Let's say that the Earth is 14 billion years old today and that 2 photons from a light source 14 billion light years from us sent 2 photons towards the Earth 14 billion years ago. (4.41504e17seconds)

Both photons followed exactly the same path.

Allice received both of these photons today. – She reflected the one photons to Bob.

Alice lives on top of a skyscraper which is 1000 meters high. Bob lives on the first floor.

Bob's clock loses 1e-15 seconds every second compared to Alice's clock.

Alice agrees with the theory of relativity that the speed of light is 3e8 m/s and she also agrees that the distance that the photon she received has travelled excatly: 14 billion light years.

But Bob disagrees with Alice, - well it took the photon 1/300,000 second longer to reach him at 1st floor, because - (after Alice reflected one of the photon to him) - the photon had to travel an extra 1000 meter  .

The problem is that Bob's watch shows that the photon has travelled 441 seconds less than the time Alice has measured.

(4.41504e17seconds x loss of time factor 1e-15)

Now who is right

Alice, who 100% agrees with the theory of relativity?

Or Bob?

If Bob is right, then either the distance to the source that emitted the photon must be 132300000 km shorter than the distance that Alice has agree about, - OR - the speed of light must be faster than c, at least for Bob .

or what ?

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15 minutes ago, Bjarne-7 said:

or what ?

Or set the problem out correctly, filling in the missing lines telling us where your figures come from and showing us how exactly the two photons can have followed exactly the same path (world line ?)

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21 minutes ago, studiot said:

Or set the problem out correctly, filling in the missing lines telling us where your figures come from and showing us how exactly the two photons can have followed exactly the same path (world line ?)

It's a thought experiment. Photons can theoretically be fired from the same "cannon", in the exact same direction and with an insignificant split-second interval.

29 minutes ago, Bjarne-7 said:

If Bob is right, then either the distance to the source that emitted the photon must be 132300000 km shorter than the distance that Alice has agree about, - OR - the speed of light must be faster than c, at least for Bob .

I assume that the speed of light does not change because the 2 photons travel the same path.
I also don't expect the distance to change, again because the 2 photons travel by the same path.
The only rational / logical question that remains is therefore, is it possible that rulers may be relativistic variants?
Edited by Bjarne-7
writting error
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2 hours ago, Bjarne-7 said:

It's a thought experiment. Photons can theoretically be fired from the same "cannon", in the exact same direction and with an insignificant split-second interval.

If they are sent in the same exact direction, how do observers at transversely-separated locations each get a photon?

As to the scenario: do the two observers agree on the speed of light? Their clocks will disagree, and each will get the correct value of c when measured locally. What implications does that have?

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3 hours ago, Bjarne-7 said:

The problem is that Bob's watch shows that the photon has travelled 441 seconds less than the time Alice has measured.

So why is that a problem ?

Bob is at the bottom of a gravity well, compared to Alice, so expects his clock to run more slowly.

But you haven't demonstrated that your figures are correct for the time of flight and height difference.

Edited by studiot
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2 hours ago, swansont said:

If they are sent in the same exact direction, how do observers at transversely-separated locations each get a photon?

Alice will reflect photon-2 , - 90 degree to Bob

2 hours ago, swansont said:

As to the scenario: do the two observers agree on the speed of light? Their clocks will disagree, and each will get the correct value of c when measured locally. What implications does that have?

The path that the two photons travel is exactly the same (except the last 1000 meter) . The time measured is different, - this is a fact, -  thus either c, - distance, - cannot be t the same for both Alice and Bob. Or the ruler must be a variant.

1 hour ago, studiot said:

But you haven't demonstrated that your figures are correct for the time of flight and height difference.

It is assumed that both photons follow the same route all the way to Alice.
In principle, we could imagine that there is only 1 photon, and that Alice measures the travel time it took that one photon, - at the exact moment when she reflects this one photon further on to Bob.

On the one hand Alice will  measure the travel time to be 1/300,000 of a second longer for the Photon to reach Bob.

However, on the other hand Bob can confirm that the journey took 41 seconds less than the time Alice has measured.

So the consequence must be that Bob and Alice will never be able to agree, unless either: - the travel distance , - or c, - must be perceived differently by Alice and Bob

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43 minutes ago, Bjarne-7 said:

So the consequence must be that Bob and Alice will never be able to agree

That's correct.  They will not agree on the time the photon was emitted nor the distance, even taking into account the extra distance the photon traveled.

Edited by Bufofrog
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19 minutes ago, Bufofrog said:

That's correct.  They will not agree on the time the photon was emitted or the distance, even taking into account the extra distance the photon traveled.

That was going to be my next question.  +1

56 minutes ago, Bjarne-7 said:

It is assumed that both photons follow the same route all the way to Alice.
In principle, we could imagine that there is only 1 photon, and that Alice measures the travel time it took that one photon, - at the exact moment when she reflects this one photon further on to Bob

But the issue here is

How do Bob and Alice know when to start their clocks ticking ?

Obviously they must have lived 14 thousand million years in order to make the measurement, plus a little bit to build their clocks and synchronise them.

Edited by studiot
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16 minutes ago, Bufofrog said:

That's correct.  They will not agree on the time the photon was emitted or the distance, even taking into account the extra distance the photon traveled.

We now assume there is only 1 photon, it is less confusing.
The photon can only be emitted at the same moment.
Alice and Bob can easily agree to start their timing at the same moment.

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2 minutes ago, studiot said:

Obviously they must have lived 14 thousand million years in order to make the measurement, plus a little bit to build their clocks and synchronise them.

This is a thought experiment so some idealization is ok, I think.  It seems to me that this is a classic frame mixing problem.  The OP says the photon was emitted exactly 14 billion years ago.  But according to who's clock?  I think that the OP is assuming Alice's clock.  Then for Bob the OP mixes Alice's frame and Bob's frame together to get a nonsensical answer.

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4 minutes ago, Bjarne-7 said:

Alice and Bob can easily agree to start their timing at the same moment.

No, they cannot because of relativity of simultaneity.

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40 minutes ago, studiot said:

How do Bob and Alice know when to start their clocks ticking ?

Obviously they must have lived 14 thousand million years in order to make the measurement, plus a little bit to build their clocks and synchronise them.

A photon sent from the same source, - 14 billion years earlier, - by the same path, can signal Bob and Alice to start timing when this first photon is received.

PS. I am not allowed to post more that 5 post today, so I have to take a brake

In the meantime, consider that , we can also imagine that the photon is simply trapped in a skyscraper and reflected between Alice and Bob, endlessly up and down for 14 billion years.
The problem is the same.
Bob and Alice cannot agree on how far the photon has traveled in 14 billion years.
It will not make sense to claim that there is a 41 second difference between Alice's and Bob's perception of simultaneity.

Edited by Bjarne-7
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1 hour ago, Bjarne-7 said:

It will not make sense to claim that there is a 41 second difference between Alice's and Bob's perception of simultaneity.

Why not ? you are just dressing up incredulity as something more; I still don't see a problem.

I haven't checked your numbers but it is an observed fact that clocks lower in a gravity well run more slowly so Bob will record less elapsed time for the same interval.

Edited by studiot
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6 hours ago, Bjarne-7 said:

Alice lives on top of a skyscraper which is 1000 meters high. Bob lives on the first floor.

Bob's clock loses 1e-15 seconds every second compared to Alice's clock.

It sounds like the question is only about gravitational time dilation, not about inertial frames or relativity of simultaneity.

Bob and Alice agree that the local speed of light is c. They don't say "I can measure the speed of light in empty space using measurements I'm making locally in a gravitational well." Bob errs in doing so.

Another way to say it is, "the coordinate speed of light isn't always c", however I don't know if "coordinate speed" (as in, measuring d and t using a distant observer's coordinates) is a standard term.

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3 hours ago, Bjarne-7 said:

We now assume there is only 1 photon, it is less confusing.
The photon can only be emitted at the same moment.
Alice and Bob can easily agree to start their timing at the same moment.

Even if they could, we know their clocks run at different rates, owing to GR. What, precisely, is the problem?

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3 hours ago, md65536 said:

It sounds like the question is only about gravitational time dilation, not about inertial frames or relativity of simultaneity

I should not have used the term frame that was not correct.  Bob and Alice are in different gravitational potentials and therefore their clocks tick at different rates.

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22 hours ago, md65536 said:

It sounds like the question is only about gravitational time dilation, not about inertial frames or relativity of simultaneity.

Correct

22 hours ago, md65536 said:

Bob and Alice agree that the local speed of light is c.

Correct

22 hours ago, md65536 said:

They don't say "I can measure the speed of light in empty space using measurements I'm making locally in a gravitational well." Bob errs in doing so.

Another way to say it is, "the coordinate speed of light isn't always c", however I don't know if "coordinate speed" (as in, measuring d and t using a distant observer's coordinates) is a standard term.

We cannot conclude that Bob is doing something "wrong", but only that Bob does not agree with Alice, because Bob has measured the travel time for the same photon to be shorter than Alice.

20 hours ago, swansont said:

Even if they could, we know their clocks run at different rates, owing to GR. What, precisely, is the problem?

Both Alice and Bob measure an event taking place in outer space. - Neither of them is part of the event apart from the fact that they both measure the arrival of the same photon to Earth. But Bob and Alice get 2 different results. (Bob measures the photons journey to take 41 seconds less than the time Alice has measured. ) - This must mean that either c must be a variant and/or Bob and Alice ruler must be a variant. Which of these 2 factors is changing in a gravitational field?

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1 hour ago, Bjarne-7 said:

Both Alice and Bob measure an event taking place in outer space. - Neither of them is part of the event apart from the fact that they both measure the arrival of the same photon to Earth. But Bob and Alice get 2 different results. (Bob measures the photons journey to take 41 seconds less than the time Alice has measured. ) - This must mean that either c must be a variant and/or Bob and Alice ruler must be a variant. Which of these 2 factors is changing in a gravitational field?

Observers in different gravitational potentials do not agree on the speed of light. Spacetime is not flat, and clocks run at different rates.

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1 hour ago, Bjarne-7 said:

This must mean that either c must be a variant and/or Bob and Alice ruler must be a variant. Which of these 2 factors is changing in a gravitational field?

If Bob made no mistake then he or she understands that a local clock is ticking at a different rate than a clock in empty space, and that light traveling through empty space at a speed of c according to a clock in empty space, is not going to give the same result when using clocks that are ticking at different rates. You measure the time of light's journey according to conditions all along the journey, not just those at the end.

(In SR this would be different, because with everything assumed to be empty space, the conditions at the end are the same as conditions throughout the journey.)

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2 hours ago, swansont said:

Observers in different gravitational potentials do not agree on the speed of light.

Well they would agree on the speed of light, wouldn't they? They would disagree on the frequencies and wave numbers, or IOW, the number of cycles a particular physical interval contains.

I'm a little confused with the initial setting of the problem, as I see no reason why Alice and Bob should agree on anything, as they see different things.

But I take it that the OP is trying to reformulate the problem for just one photon.

But maybe I misunderstood the whole thing, so I'll take some more time tomorrow.

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9 hours ago, swansont said:

Observers in different gravitational potentials do not agree on the speed of light. Spacetime is not flat, and clocks run at different rates.

Correct, they can't possibly do that

9 hours ago, md65536 said:

If Bob made no mistake then he or she understands that a local clock is ticking at a different rate than a clock in empty space, and that light traveling through empty space at a speed of c according to a clock in empty space, is not going to give the same result when using clocks that are ticking at different rates. You measure the time of light's journey according to conditions all along the journey, not just those at the end.

(In SR this would be different, because with everything assumed to be empty space, the conditions at the end are the same as conditions throughout the journey.)

Right, the problems is not limited to Bob and Alice.
Bob and Alice cannot agree about any speed or any distance anywhere in the universe or even at planet Earth, - except in their own gravitational environment.

8 hours ago, joigus said:

Well they would agree on the speed of light, wouldn't they? They would disagree on the frequencies and wave numbers, or IOW, the number of cycles a particular physical interval contains.

I'm a little confused with the initial setting of the problem, as I see no reason why Alice and Bob should agree on anything, as they see different things.

But I take it that the OP is trying to reformulate the problem for just one photon.

But maybe I misunderstood the whole thing, so I'll take some more time tomorrow.

You have good reason to be confused.
Remember that the "problem" is not limited to the speed of light. No matter how Bob and Alice tries to relate to distances or speeds in other gravitational environments, they encounter the same problem over and over again.
They pretty much always disagree about speeds and distances everywhere in the universe.

Imagine that Bob and Alice have measured the orbital period of Saturn's orbit.
Bob will naturally say that the orbit-time he has measured is a split second shorter than what Alice has measured.
Bob must of course then conclude that this means that the orbit must be shorter than what Alice can conclude, -  t * v = d

Einstein would probably answer that Bob and Alice must both be right, but it seems that Einstein forgot to tell why?

No one will properly dispute that the distance being  "d"  must be firmly anchored.
We know that Bob and Alice define "t" differently, and hence also necessarily must define "v" differently.

"v" consists of: - meters "m" per second "s".
The only remaining parameter left to  "manipulate" is therefore "m" - (the ruler).

We need to deal with this rationally, logically and mathematically.
And must conclude that different perception of "deformable distances" can not only be due to variation of "t", - but also must include "m", (the ruler)  which then must be considered as a proportional relativist variant.

This is the only mathematical possibility which can allow Bob and Alice to explain that they measure distances differently.

It means when time in a gravitational environment stretches, there is a proportional corresponding stretch of the ruler too.

In other words, Bob and Alice rulers are absolutely the same length when they come from the factory.
But when Bob and Alice bring them to different gravitational environments, the rulers are changing size (stretching)  proportionally with the change / stretch of time.

Only this solution can justify the claim that both Bob and Alice are right. The alternative is that nobody is right.. maybe only except for Peter who lives infinitely far away in a environment completely without any gravitation, which means far far far far away.

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I don’t actually see what the supposed “problem”, that the title of this threads alludes to, is meant to be. In curved spacetimes, observers will, in general, not agree on quantities that aren’t either tensors, or invariants formed from them. Therefore we do not, in general, expect observers to agree on specific measurements of space, time, energy, momentum etc - but they will always agree on the metric, and thus spacetime intervals and everything that derives from this. That’s just basic differential geometry.

So could you just simply state what you think the “problem” is with this, preferably without getting lost in the intricacies of some specific scenario?

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16 minutes ago, Markus Hanke said:

I don’t actually see what the supposed “problem”, that the title of this threads alludes to, is meant to be. In curved spacetimes, observers will, in general, not agree on quantities that aren’t either tensors, or invariants formed from them. Therefore we do not, in general, expect observers to agree on specific measurements of space, time, energy, momentum etc - but they will always agree on the metric, and thus spacetime intervals and everything that derives from this. That’s just basic differential geometry.

So could you just simply state what you think the “problem” is with this, preferably without getting lost in the intricacies of some specific scenario?

Purely mathematically, we have to deal with whether the physical meter is a deformable variable or not, just as we once had to (first theoretically) deal with, - and finally recognize that the passage of time is a provable variable. It is not satisfactory that we then have to close our eyes as soon as things become a little bit complicated or challenging. Constantly asking new questions is what science is all about

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8 minutes ago, Bjarne-7 said:

Purely mathematically, we have to deal with whether the physical meter is a deformable variable or not

In curved spacetimes, measurements of spatial distance, just like measurements of time, generally depend on the observer, because those are not tensorial quantities. Only spacetime intervals are. This is well understood, and the mathematics of differential geometry on Riemann manifolds predate GR.

Exactly where is the problem with this?

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24 minutes ago, Markus Hanke said:

In curved spacetimes, measurements of spatial distance, just like measurements of time, generally depend on the observer, because those are not tensorial quantities. Only spacetime intervals are. This is well understood, and the mathematics of differential geometry on Riemann manifolds predate GR.

Exactly where is the problem with this?

The problem arises exactly as soon as you mathematically compare Bob's and Alice's rulers. Try to isolate your thinking to it.

And remember that there is no guarantee that the current theory of relativity is the final version.

If the ruler is a propotional relatevistic variable the theory of relativty must be modified according to that

Edit

Can you disprove that he ruler is a proportional relativistic variable ? If not this is an possible option.

Edited by Bjarne-7
Edit

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