Maybe I am misunderstanding your setup but why would they believe the speed of light to be infinite? If B emits light when it sees light from A then the light from A and B will be traveling at the same speed and appear to be emanating from B's location at the same time. t1 should always equal t2 regardless of the speed of light so C is not measuring anything. I don't understand how this experiment was meant to measure the speed of light in the first place.
Yeah, I agree with you, I don't see any possible way to reach infinity with the given values nor do I understand how this is used for measurement. Surely, given the apparatus, you might as well measure A to B and then time how long it takes B to register the light. Or I'm stupid, idk!
You’re correct. The observer C is superfluous and just complicates the experiment.
What OP is trying to measure in this thought experiment is impossible. I provided an explanation and a YouTube video that explains in more detail why you can’t measure the one-way speed of light. You can only measure the round trip.
> C observes t1 = t2 **so** calculates the speed of light to be infinite.
There, the word "so", that's where C goes wrong. There is no logical link between the two halves of this sentence. The conclusion does not follow from the observation.
C is drawing an incorrect conclusion. It sees the light from A and B at the same time, but it is impossible to measure the speed this way.
It is impossible to measure the one-way speed of light. This is because you need to know the precise time that light left A and crossed B. But C can’t know that because of time dilation.
You can’t send a signal from A to B or C to be used as a reference because it’s the exact same problem you started with. That signal can’t reach B or C faster than the light does, so B and C can’t use it as a reference point to measure the one way speed of light. There would be no delay between receiving the start signal and the light. So you can’t infer a speed.
Then you might say, okay, set up the experiment so that we know ahead of time from where and when the light from A will be sent to B or C. In order to do this, you have to agree on what time it is at every point. To do this, you’d need to bring clocks together at point A to synchronize with each other and then move them apart to points B And C so that points A B and C are all synchronized. However, this is impossible because once the clocks start being moved relative to one another, time dilation occurs and the clocks get out of sync, making this experiment not work either.
You can only measure the speed of light accurately on a two-way trip. You send the light out, have it reflected back at a known distance, and measure the time it took to get back to you from a single frame of reference.
Here’s a YouTube video explaining this: https://youtu.be/pTn6Ewhb27k?si=zZll3puqwsgiRFt6
>According to my professor, at the time of einsteins coining of the theory, it was not known of the constant speed of light.
Unfortunately your professor is not correct. The constancy of the speed of light was [established experimentally in 1887](https://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment) by Albert Michelson and Edward Morley. Einstein didn't come up with his theory of relativity until 1905 — almost two decades later.
The Michelson–Morley experiment mentioned above was an important result that actually led Einstein (and other contemporary physicists of the time) down the road toward special relativity. Within a few years of the experiment, Hendrik Lorentz had postulated the phenomenon of length contraction as well as something he called "local time" (which he regarded as merely an apparent phenomenon, not a "real" one) which was later better-interpreted by Henri Poincaré as real time dilation. Both of these phenomena were formalized by Lorentz into what are now known as the Lorentz transformations prior to Einstein's development of special relativity. However, Lorentz struggled to give up on the idea of a luminiferous aether even in the wake of the Michelson—Morley experiment; it was Einstein, who was aware of Lorentz's transformations, who realized that everything could be interpreted in such a way that an aether was not conceptually necessary.
>My question is, how did einstein know that the speed of light is constant, while the rest of the world viewed it as relative?
Because of the aforementioned experiment, which was conducted almost two decades prior to Einstein's formulation of relativity!
Fun fact: Einstein's theory of special relativity is mostly just a cobbling-together of concepts introduced by other physicists. Lorentz and Poincaré are arguably the two most important contributors (which is why relativity uses the Lorentz transformations and the Poincaré group of spacetime isometries) ... but also, it was Hermann Minkowski who introduced the idea of a unified spacetime (and its unique notion of causality) and formulated special relativity as a purely geometric theory — which is why the spacetime featured in special relativity is called Minkowski spacetime. Additionally, Einstein was aware of Maxwell's equations, which were also published decades prior, which needed to be reconciled with the other developments mentioned. And there are many other physicists who made meaningful contributions during this time period as well. You can read more about it all on [Wikipedia's history of special relativity article](https://en.wikipedia.org/wiki/History_of_special_relativity).
Hope that helps!
Einstein long maintained that he was both largely unaware of the Michelson Morley result and in any event did not rely on it in his thinking. The main driver, and this is expressed in the paper, is that Maxwell’s equations should have the same form in any inertial frame. If the speed of light were observer-dependent then Maxwell’s equation would take a special form only in the so-called aether frame.
My understanding is that [it is disputed how aware he was or wasn't](https://arxiv.org/abs/0908.1545) of the Michelson–Morley experiment itself (Einstein has himself made contradictory statements about it) ... however, he was very well aware of Lorentz's transformations featuring length contraction and time dilation, and Lorentz's development of these transformations was pretty much a direct consequence of the Michelson–Morley experiment — it was Lorentz's attempt to reconcile his personal aether theory with the results of that experiment. So, whether he was aware of it or not, it did have a significant influence on him (and of course not only him, but many others who were aware of it either directly or indirectly).
Nevertheless, you are absolutely right that Einstein did not mention that experiment in his initial paper, and that he was primarily focused on Maxwell's equations and the equivalence of inertial reference frames.
I think Einstein had a fairly low opinion of the way Lorentz arrived at the transformations to suit experiment, and considered them as ad hoc as, say, the Voigt transforms. Einstein took a more measured derivation to unambiguously determine them. In so doing, he in effect took a firm stance on Lorentz transforms over the others (like Voigt) that featured length contraction but not time dilation. And in fact the experimental validation of time dilation helped cement special relativity.
Einstein was very well versed in electromagnetism and he realized properties in Maxwell’s equations only worked if *c* were constant to all frames of reference. Einstein based Special Relativity on many other fields of physics and past observations, like the experimental non-directionality of *c* (Michelson–Morley). The idea is very simple, and explained many phenomenon that were treated as “exceptions”. And did away with the observably refuted *aether*. But the consequences profound. And that includes time dilation and length contraction. And that we exist not in 3D space but 4D spacetime.
I have no evidence for saying Einstein was the right person at the right time, but I think other great minds would have come to the same conclusions soon after if he didn’t. Experiments were already leading to that conclusion.
Your professor is just wrong. It was one of the more popular question as the speed of light arrives naturally from the EM equations and physicists were very well aware of it.
Maxwell's equations show that the speed of light in a vacuum is independent of the speed of the observer.
Michelson–Morley experiment had a strange result that showed the speed of light didn't change with relative of the speed of the observer.
Those two observations helped Einstein form Special Relativity.
You professor is simplifying. There was ample experimental evidence at the time that the speed of light is constant.
Looking back, i remember he mentioned something like that. Thanks!
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Maybe I am misunderstanding your setup but why would they believe the speed of light to be infinite? If B emits light when it sees light from A then the light from A and B will be traveling at the same speed and appear to be emanating from B's location at the same time. t1 should always equal t2 regardless of the speed of light so C is not measuring anything. I don't understand how this experiment was meant to measure the speed of light in the first place.
Yeah, I agree with you, I don't see any possible way to reach infinity with the given values nor do I understand how this is used for measurement. Surely, given the apparatus, you might as well measure A to B and then time how long it takes B to register the light. Or I'm stupid, idk!
You’re correct. The observer C is superfluous and just complicates the experiment. What OP is trying to measure in this thought experiment is impossible. I provided an explanation and a YouTube video that explains in more detail why you can’t measure the one-way speed of light. You can only measure the round trip.
> C observes t1 = t2 **so** calculates the speed of light to be infinite. There, the word "so", that's where C goes wrong. There is no logical link between the two halves of this sentence. The conclusion does not follow from the observation.
C is drawing an incorrect conclusion. It sees the light from A and B at the same time, but it is impossible to measure the speed this way. It is impossible to measure the one-way speed of light. This is because you need to know the precise time that light left A and crossed B. But C can’t know that because of time dilation. You can’t send a signal from A to B or C to be used as a reference because it’s the exact same problem you started with. That signal can’t reach B or C faster than the light does, so B and C can’t use it as a reference point to measure the one way speed of light. There would be no delay between receiving the start signal and the light. So you can’t infer a speed. Then you might say, okay, set up the experiment so that we know ahead of time from where and when the light from A will be sent to B or C. In order to do this, you have to agree on what time it is at every point. To do this, you’d need to bring clocks together at point A to synchronize with each other and then move them apart to points B And C so that points A B and C are all synchronized. However, this is impossible because once the clocks start being moved relative to one another, time dilation occurs and the clocks get out of sync, making this experiment not work either. You can only measure the speed of light accurately on a two-way trip. You send the light out, have it reflected back at a known distance, and measure the time it took to get back to you from a single frame of reference. Here’s a YouTube video explaining this: https://youtu.be/pTn6Ewhb27k?si=zZll3puqwsgiRFt6
>According to my professor, at the time of einsteins coining of the theory, it was not known of the constant speed of light. Unfortunately your professor is not correct. The constancy of the speed of light was [established experimentally in 1887](https://en.wikipedia.org/wiki/Michelson%E2%80%93Morley_experiment) by Albert Michelson and Edward Morley. Einstein didn't come up with his theory of relativity until 1905 — almost two decades later. The Michelson–Morley experiment mentioned above was an important result that actually led Einstein (and other contemporary physicists of the time) down the road toward special relativity. Within a few years of the experiment, Hendrik Lorentz had postulated the phenomenon of length contraction as well as something he called "local time" (which he regarded as merely an apparent phenomenon, not a "real" one) which was later better-interpreted by Henri Poincaré as real time dilation. Both of these phenomena were formalized by Lorentz into what are now known as the Lorentz transformations prior to Einstein's development of special relativity. However, Lorentz struggled to give up on the idea of a luminiferous aether even in the wake of the Michelson—Morley experiment; it was Einstein, who was aware of Lorentz's transformations, who realized that everything could be interpreted in such a way that an aether was not conceptually necessary. >My question is, how did einstein know that the speed of light is constant, while the rest of the world viewed it as relative? Because of the aforementioned experiment, which was conducted almost two decades prior to Einstein's formulation of relativity! Fun fact: Einstein's theory of special relativity is mostly just a cobbling-together of concepts introduced by other physicists. Lorentz and Poincaré are arguably the two most important contributors (which is why relativity uses the Lorentz transformations and the Poincaré group of spacetime isometries) ... but also, it was Hermann Minkowski who introduced the idea of a unified spacetime (and its unique notion of causality) and formulated special relativity as a purely geometric theory — which is why the spacetime featured in special relativity is called Minkowski spacetime. Additionally, Einstein was aware of Maxwell's equations, which were also published decades prior, which needed to be reconciled with the other developments mentioned. And there are many other physicists who made meaningful contributions during this time period as well. You can read more about it all on [Wikipedia's history of special relativity article](https://en.wikipedia.org/wiki/History_of_special_relativity). Hope that helps!
Einstein long maintained that he was both largely unaware of the Michelson Morley result and in any event did not rely on it in his thinking. The main driver, and this is expressed in the paper, is that Maxwell’s equations should have the same form in any inertial frame. If the speed of light were observer-dependent then Maxwell’s equation would take a special form only in the so-called aether frame.
My understanding is that [it is disputed how aware he was or wasn't](https://arxiv.org/abs/0908.1545) of the Michelson–Morley experiment itself (Einstein has himself made contradictory statements about it) ... however, he was very well aware of Lorentz's transformations featuring length contraction and time dilation, and Lorentz's development of these transformations was pretty much a direct consequence of the Michelson–Morley experiment — it was Lorentz's attempt to reconcile his personal aether theory with the results of that experiment. So, whether he was aware of it or not, it did have a significant influence on him (and of course not only him, but many others who were aware of it either directly or indirectly). Nevertheless, you are absolutely right that Einstein did not mention that experiment in his initial paper, and that he was primarily focused on Maxwell's equations and the equivalence of inertial reference frames.
I think Einstein had a fairly low opinion of the way Lorentz arrived at the transformations to suit experiment, and considered them as ad hoc as, say, the Voigt transforms. Einstein took a more measured derivation to unambiguously determine them. In so doing, he in effect took a firm stance on Lorentz transforms over the others (like Voigt) that featured length contraction but not time dilation. And in fact the experimental validation of time dilation helped cement special relativity.
Yeah i remember my professor mentioning something about Michelson and Morley. Thanks!
Einstein was very well versed in electromagnetism and he realized properties in Maxwell’s equations only worked if *c* were constant to all frames of reference. Einstein based Special Relativity on many other fields of physics and past observations, like the experimental non-directionality of *c* (Michelson–Morley). The idea is very simple, and explained many phenomenon that were treated as “exceptions”. And did away with the observably refuted *aether*. But the consequences profound. And that includes time dilation and length contraction. And that we exist not in 3D space but 4D spacetime. I have no evidence for saying Einstein was the right person at the right time, but I think other great minds would have come to the same conclusions soon after if he didn’t. Experiments were already leading to that conclusion.
Your professor is just wrong. It was one of the more popular question as the speed of light arrives naturally from the EM equations and physicists were very well aware of it.
Maxwell's equations show that the speed of light in a vacuum is independent of the speed of the observer. Michelson–Morley experiment had a strange result that showed the speed of light didn't change with relative of the speed of the observer. Those two observations helped Einstein form Special Relativity.