I know the one-way speed of light question has been exhausted, and I'm sorry for the naive question, but I would like to understand one thing. Can we measure the one-way speed of anything at all? If we "truly" can, why can't we synchronize that thing and an emission of light from one place to another to compare their speeds? For instance, and for simplicity sake assume 2 cars pass a point at exactly the same time and we know one car is going 60 mph and we do not know the speed of the other car. We could set up a clock 60 miles away, knowing that the car going 60 will take one hour to get there. Then,by using only one clock and by checking the difference in arrival times, we could calculate the second car's speed. Why can't we do something similar with light and another medium. Even if it needed to be sent from some space shuttle to the ISS, it seems like with modern equipment, we should be able to get some decent approximation of the one way speed.
6 Answers
Can we measure the one-way speed of anything at all?
No, there is nothing unique to light in that respect. To measure a one-way speed of anything requires that you allow it to travel over a known distance with a start and stop time measured at the beginning and end of the known distance. Doing so requires that the start and stop clocks must be synchronized. Different clock synchronization conventions will produce different one way speeds. Since any valid synchronization convention can be used, the one way speed simply reflects your choice of convention.
- 117,350
In practice, yes. How much the time coordinate in a "reasonable" anisotropic coordinate system ("reasonable" meaning things like "things don't arrive before they leave") changes over a certain distance, compared to an isotropic coordinate system, can't be more than the spatial separation divided by c. In other words, suppose your car travels 100 feet per second (about 68 mph), or about one light nanosecond per second. That is, for every second in an isotropic coordinate system, its position in that coordinate system changes by one billionth of a light-second. Then an anisotropic coordinate system could say that it actually took (1+1/billion) seconds to travel that distance, or that it took (1-1/billion) seconds.
So we can't measure the exact one-way speed, but we can measure it precisely enough as to not make a difference for most practical purposes. (You're not going to get out of a speeding ticket by arguing that there's an anisotropic coordinate system in which you were going 30 mph rather than 60 mph. I mean, that wouldn't work even if there were some such coordinate system, but there isn't one anyway.)
But from a theoretical point of view, the exact one-way speed does depend on the coordinate system, even for a car. The difference between light and a car is that while, for a car, distance/c is miniscule compared to the time it takes to travel that distance, for light it is not. Light travels one light second per second in isotropic coordinate systems, so the time that it takes to travel one light second in an anisotropic coordinate system can vary from 1+1 seconds (giving a speed of c/2) to 1-1 (giving a speed of infinity). And if you try to measure the speed of light by using the speed of a car, the math is going to be such that that miniscule difference between isotropic and anisotropic speeds is actually going to matter.
Like a lot of things in relativity (time dilation, length contraction, etc.), uncertainty in one-way speeds technically exist at any non-zero speed, but in practice it can be ignored for most purposes unless the speed is a significant fraction of c.
- 9,687
Measure the length of a finite segment of train track. Start your chronometer when you see the train enter the segment, stop it when it left the segment. If the train was travelling at constant speed you can determine it by calculating length/time.
The reason why this does not work with the one-way speed of light is because light is the thing that you want to measure.
A more sophisticated version is to use Doppler shift, if an ambulance with its sirens on (and you know the frequency of the siren), you can determine its speed by noticing the shift in sound frequency.
As other comments suggest, of course all these measurements and formulas depend on your convention on the one-way speed of light to establish space-time reference frames. Given a convention you can measure the one-way speed of anything that does not travel at the speed of light.
- 6,886
I would say no. One of the most fascinating things in physics is time dilation. The speed of light is always the same but the speed of time varies. Not only may A and B be in different time frames as illustrated by others but also at different rates of time change. One way to visualize this is here on earth. It is scientifically theorized that the center of earth is 2 1/2 years younger than the surface of the earth due to time dilation. so first of all which is the correct time? Now if you could send a light to the center of the earth and reflect it back to the surface you begin to see the problem. Even though the speed of light would be the same weather it’s traveling there or traveling back, the actual time and the speed of time would be completely different at both ends.
- 4,159
You are aware of this issue of the conventionality of simultaneity or the definitions there in of what the actual one-way speed of light is. That we can define different values for it, making it anisotropic, but in a manner that gives rise to all the same observations that the Special Theory of Relativity ends up covering. The issue is much more deeper than just the one-way speed of light and this conventionality could be applied to all of known physics.
Einstein had actually considered such a general conventionality that went beyond light and he discussed this in a speech he gave. A paper discussing this and making its own conclusions on the matter about his perspective is given here.
To make a claim about the speed of an object requires a measure of time (counting periodic occurrences) and a measure of the distance it travels. The problem in most situations is that the assumptions regarding the constancy of its speed in the outgoing then the coming back parts of its journey are assumptions that heavily depend on what our dynamics are and our spacetime structure. You could assume some background spacetime structure and some assumption about the dynamics of objects leading to certain somewhat unobservable conclusions (inferred results). You could, however, change our spacetime structure and change the way objects/particles/fields interact with each other leading to similar observable results but different unobservables. Such as the inferred speed of the object at any point along its trajectory or the distance it really traveled.
So it may be the case that the speed of many objects, even ordinary ones, may be fairly conventional. Dependent on our arbitrary assumptions regarding spacetime structure and dynamical interactions.
According to Derek Muller from Veritasium, no:
https://www.youtube.com/watch?v=pTn6Ewhb27k&ab_channel=Veritasium
At this point in time, we are measuring the 'average' speed of the roundtrip of light. This is due to the problem of needing two points in space to measure speed:
Speed = Distance/Time
So you would need to send off a beam of light from Point A and simultaneously tell Point B that you've started recording. This would need to happen at a speed faster than what we know as light-speed. Which is impossible.
- 987