# Parallel light reflection for a one-way speed of light measurement setup

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• OWSOL

#### OWSOL

Hello,

Is there a mirror that will reflect light in parallel trajectories ?

If yes, is the reflected light in sync, and will all beams hit a flat surface simultaneously ?

Thank you

## Answers and Replies

Is there a mirror that will reflect light in parallel trajectories ?
Certainly. Both a flat mirror and a curved mirror can depending on context. For example, a parabolic mirror will reflect light rays in a parallel bundle if they are emitted by a source located at the mirrors focal point.

If yes, is the reflected light in sync, and will all beams hit a flat surface simultaneously ?
No, not unless the light is already parallel and strikes a flat surface at a 90 degree angle. Any deviation in angle will cause the beams to strike the surface at different times.

vanhees71
Hello Drakkith,

Thank you for the reply.

So, if a source, situated exactly at a parabolic mirror's focal point, emits a light pulse that reflects towards a perfectly flat surface which is parallel to the mirror, can we make the assumption that the reflected rays hit the surface simultaneously ?

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So, if a source, situated exactly at a parabolic mirror's focal point, emits a light pulse that reflects towards a perfectly flat surface which is parallel to the mirror, can we make the assumption that the reflected rays hit the surface simultaneously ?
To within a fraction of a wavelength depending on the quality of your optical surfaces, yes.

So, if a source, situated exactly at a parabolic mirror's focal point, emits a light pulse that reflects towards a perfectly flat surface which is parallel to the mirror, can we make the assumption that the reflected rays hit the surface simultaneously ?
Yes. The definition of a parabola is that the distance from any point to the focus (##F##) is the same as the perpendicular distance to the directrix. So, in the drawing below ##\bar {FP}## = ##\bar {PD}## is the definition. For a distant plane the light will travel a distance of ##\bar {FP}## + ##\bar {PQ}## = ##\bar {DP}## + ##\bar {PQ}## = ##\bar {DQ}## since those are colinear. Then this distance must have no dependence on the location of point P (no x dependence).

This is drawn in 2D, but it's the same in 3D, like a real dish antenna.

It is true that a paraboloid generates an equi-phase wave front across its aperture, but where the wavelength is significant compared to the reflector diameter, we can see some interference effects depending on distance and the size of the screen.

Dale, DaveE and Ibix
It is true that a paraboloid generates an equi-phase wave front across its aperture, but where the wavelength is significant compared to the reflector diameter, we can see some interference effects depending on distance and the size of the screen.
This is (should be) a more general disclaimer. There are always diffraction limits in optics when things get small or when you look carefully. Parabolas and/or other things.

Hello all,

The reason I started this thread is to gain knowledge on a way to have two perfectly aligned, horizontally spaced clocks, simultaneously stopped.

So, I thought of the light emitted from a source, placed at the focus point of a parabolic mirror reflecting towards two clocks that are horizontally spaced at distance x, and parallel to the mirror.

Using the most accurate equipment available, is this a usable setup for further measurements ?

thank you

The reason I started this thread is to gain knowledge on a way to have two perfectly aligned, horizontally spaced clocks, simultaneously stopped.
You can stop them to within some time interval of each other, with that time interval being more or less depending on your setup. A simple electrical signal passed through wires to each clock will stop them so close to each other that your limiting factor is probably not the stopping device itself, but the accuracy of most clocks. As to what the alignment of each clock has to do with anything, I'm unsure.

So, I thought of the light emitted from a source, placed at the focus point of a parabolic mirror reflecting towards two clocks that are horizontally spaced at distance x, and parallel to the mirror.
Just scrap the mirror altogether and place the clocks equidistant from the light source.

Using the most accurate equipment available, is this a usable setup for further measurements ?
What are you measuring?

FactChecker and Ibix
Hello again Drakkith,

Coming back to this idea of mine and to answer your question, What are you measuring?, I can say that I am not measuring anything yet, just gathering some info to validate a one-way speed of light measurement setup.

This is a thought experiment, so it is all theoretical, and is also pretty simple to validate or dismiss. I ask if reflected light (or not, as you mention to just scrap the mirror) can hit a flat surface simultaneously across a given length, to ensure that two parallel running clocks, aligned perpendicular to the incoming beams, could/would be stopped exactly at the same time, see attached crude sketch.

That is essential to the rest of the proposed setup...

Thank you and best regards

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It will be easy to dismiss, but there is no harm in the attempt. You should ask yourself the question "what makes this different from all other unsuccessful attempts?" Have fun with it.

FactChecker
Hello hutchphd,

Thank you for the reply, do you agree that the two clocks would be stopped simultaneously ?... This is the second part of the experiment, and as I mentioned, it is essential as it makes the first part and the whole thing work.

regards

What do you mean by "simultaneously" here? How tightly do you need to control it? And why do you need this? There are some serious conceptual problems lurking if you care about precision comparable to the flight time of light between the two clocks.

FactChecker, jbriggs444 and hutchphd
Yes "simultaneous" for whom is always the issue.

FactChecker and Ibix
Hello all,

The idea of a one way measurement of the speed of light uses the previous diagram to which we add a light source that is on the same plane as the two clocks.

Both clocks are initialized and on standby, the source emits a pulse towards the clocks, after some time reaching and starting Clock 1 en route for Clock 2, and starting it after some time.

This is where the previous questions about 'simultaneously' stopping the clocks comes in;
After both clocks have been started, we then send a pulse from the mirror to the clocks to stop them. We can then deduct the elapsed time of Clock 2 from Clock 1's reading, thus getting the time it took to travel between both clocks.

Best regards

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The idea of a one way measurement of the speed of light uses the previous diagram to which we add a light source that is on the same plane as the two clocks.
Then the conceptual problems I mentioned are fatal. Your clocks are synchronised if you assume the one way speed of light is the same as the two way speed, and not synchronised otherwise. This should be obvious because it relies on your yellow light rays traveling the same distance to the left and to the right: this only takes the same time if the light is traveling left and right at the same speed. Thus your experimental setup assumes the thing you are trying to measure.

phinds and FactChecker
Hello Ibix,

Thank you again for your reply...

frankly, I am being naïve about this, as I do not assume anything firsthand, however I do believe that light travels at the same speed in all direction, isotropic, right ?

So indeed, providing we have the most accurate clocks, perfect mirror etc, I would expect elapsed times C1-C2 to yield the current value of C... I just thought it was a way to measure owsol.

Having said that, given the types of clocks we have today, what do you estimate the minimum distance between the clocks to be, in order to give a usable value of their respective readings ? I mean, is 10 meters too close to have enough measured elapsed time to properly calculate C1-C2 ?

I ask , because I have another idea I'd like to submit :-)

however I do believe that light travels at the same speed in all direction, isotropic, right ?
It's a matter of choice. You can always interpret any experiment on the assumption of isotropic light speed and anisotropic light speed. Your measured results will be the same - only your interpretation is different.
I ask , because I have another idea I'd like to submit :-)
It doesn't matter. There is no way to sneak around this. The problem is closely analogous to measuring the angle between gridlines on a blank piece of paper. No matter how clever your experimental design, somewhere you must draw the gridlines and then the angle between them is the one you decided to draw.

Having said that, given the types of clocks we have today, what do you estimate the minimum distance between the clocks to be, in order to give a usable value of their respective readings
Improving precision simply reduces the difference (stochastic and systematic error) between the value you assumed and the result you derive.

is 10 meters too close to have enough measured elapsed time to properly calculate C1-C2 ?
That's a time difference of 33nsec. A good experiment (detector, oscilloscope, etc.) can easily measure this.

But it raises the question about "...properly calculate C1-C2 ?" Also what is a meter, and what is a second? How were your instruments calibrated, etc.? More recently the speed of light (whatever it is) has become one of the basic physical quantities that defines other units, like the meter. The measurement becomes sort of arbitrary in that context. So, speed compared to what?

Others have measured the speed of light to an accuracy of about ±1 m/sec. Which, trust me, you can't replicate. This is a good thought experiment, but to really do it you will end up hopelessly bogged down with instrument calibration questions, and unit definitions, which are profound.

https://en.wikipedia.org/wiki/Speed...of_c_and_redefinition_of_the_metre_and_second

More recently the speed of light (whatever it is) has become one of the basic physical quantities that defines other units, like the meter. The measurement becomes sort of arbitrary in that context.
That would be the two way speed of light, and yes this is not measurable in SI units. One meter is defined as the distance light travels in1/300,000,000 (or so) of a second. A "measure" of two way light speed is something like "how many meters does light travel in 1s" which turns out to be "how many times the distance light travels in 1/300,000,000 of a second does it travel in one second", to which the answer is obvious.
This is a good thought experiment, but to really do it you will end up hopelessly bogged down with instrument calibration questions,
The fundamental problem is that one of the calibrations will be a choice of clock synchronisation and, explicitly or implicitly, this defines the one way speed that is measured. That's why it doesn't matter what clever tricks the OP thinks they've got - even using an older SI standard can't change the circularity of the measurement.

DaveE
Thank you both for your comments,

Sorry, don't know yet how to insert quotes, to Ibix, I say that the experiment doesn't need any clock synchronization, only accurate ones, and to DaveE, I say good to know that 10 meters is sufficient.

If we eliminate the isotropy/anisotropy from this setup and change the way both clocks are stopped from a light source to a solid shaft (as solid as needed) that has two blades, identical and perfectly aligned to each other. Those blades are in turn aligned with each clock's photo sensor.

The pulse is emitted towards Clock1, starts it and then starts Clock2 after it travels 10 meters.

At any given time after both clocks have been started, the shaft is turned by a step motor until the blades rotate in the photo sensor stopping both clocks 'supposedly simultaneously'. We then use both readings to calculate the speed.

So, no clock synchronization, and again, this is only a thought experiment using the most accurate and defect free material.

Is this a better contender ?

Regards

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weirdoguy
Sorry, don't know yet how to insert quotes
Click "Reply" to quote the whole post or highlight the part you wish to quote and click Reply in the popup.
the experiment doesn't need any clock synchronization
Then either it isn't measuring the one way speed of light or you are fooling yourself. Looking at your design, it's the latter.
change the way both clocks are stopped from a light source to a solid shaft (as solid as needed) that has two blades, identical and perfectly aligned to each other. Those blades are in turn aligned with each clock's photo sensor.
The shaft is just another way of synchronising the clocks. It doesn't work either. How "rigid" systems behave depends on your choice of isotropic or anisotropic speed of light, and believing that the shaft can (at least under some circumstances) act like a Newtonian rigid shaft is equivalent to assuming isotropy. Remember that it's held together by electromagnetic forces, and your description of their behaviour is intimately tied to your description of the behaviour of electromagnetic waves. It turns out that a rotating shaft that you would describe as rigid if you assume isotropy you would describe as twisted if you assume anisotropy. So your clocks start simultaneously if you assume isotropy and not if you assume anisotropy.

As I said before, this is not something you can sneak around by clever experimental design. The fundamental reason is that there is no separate space and time, only 4d spacetime. When you think of space and time separately, you are thinking of picking a timelike direction and calling it "time", and slicing spacetime into a stack of 3d "sheets" and calling each one "space at an instant". If you pick a time direction orthogonal to the "sheets" then you have an isotropic speed of light. If you pick a time direction that is not orthogonal to the "sheets" you have an anisotropic speed of light. That is why you can never design an experiment to detect anisotropy of the one way speed of light - whether it is isotropic or not is your choiceof how to think about spacetime and no physics depends on your choice. Changing your choice does not change your experiment, it just changes how you describe it - and it changes how you describe your kit in exactly the same way as it changes how you describe light speed.

There is no way around this. There is an infinitely deep rabbit hole of ever more complex ways to try, just like perpetual motion and squaring the circle and other such known impossibilities. I would advise you not to climb further down it because I've just explained why you will never succeed. If you didn't understand the explanation please ask, but please don't present more schemes to do the impossible - it's a waste of everybody's time.

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nasu, jbriggs444 and DaveE
If you are interested in this subject, you would do well to take a hard look at the problem of "relativity of simultaneity". How can two observers, traveling relative to each other, agree that the light reaches both sides of the mirror "simultaneously"? The answer is that they can not. If one observer sets clocks as though they are simultaneous, then the other MUST disagree.
You should be very suspicious any time you use the words "simultaneous" or "at the same time".

It may be useful to you to try to concoct schemes and then convince yourself that they are indeed equivalent to the simpler schemes that manifestly don't work. But as @Ibix notes if you simply present different versions of essentially the same scheme, you will likely be ignored here
Veritasium does a pretty good job, you may wish to look at it:

FactChecker
The reason I started this thread is to gain knowledge on a way to have two perfectly aligned, horizontally spaced clocks, simultaneously stopped.
You can certainly do that, but they will only stop simultaneously in one frame. In other frames they will not stop simultaneously.

I can say that I am not measuring anything yet, just gathering some info to validate a one-way speed of light measurement setup.
There is no such thing as a one-way speed of light measurement. The one way speed of light is a thing that you define, not a thing that you measure.

I do believe that light travels at the same speed in all direction, isotropic, right ?
There is no need to believe it, you can simply define it. If you define it as isotropic then it is since you are allowed to define it as you wish (within some constraints). The issue is just that other people are allowed to define it anisotropically and there is no measurement you can make which will prove them wrong.

I just thought it was a way to measure owsol.
There is no possible way. It is a matter of definition, not measurement.

nasu and Ibix
Ok, then, this will be my last post in this thread...

Again, not wanting any fancy setup, I just thought that what I presented was really simple and could work as a way to derive the owsol, in any frame where the setup is used.

I will re-read your replies and look at what you suggested to better understand why this wouldn't work...

Thank you all !

hutchphd
If you really want to understand the issue in depth then this reference is indispensable:

https://www.sciencedirect.com/science/article/abs/pii/S0370157397000513

On a more cursory level, the issue is that a one-way speed (of anything, not just light) is the distance traveled divided by the difference in time. Because it is a one way speed that means that the difference in time is computed at two different locations, and therefore requires a synchronization convention. You can get different values for anyone way speed simply by choosing a different synchronization convention.

There is no possible experimental way around this issue since it is part of what makes a one way speed a one way speed. You cannot have a one way speed without choosing a synchronization convention and you can choose your synchronization convention differently in order to get different one way speeds.

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DaveE, Ibix and FactChecker
Hello and sorry everyone,

I said my last post was the last but I must ask : why does my proposal require clock synchronization ?

Thank you

The term "clock synchronization" will occur in conversations that deal with "simultaneous" or "at the same time". If you say that two spatially separated events are simultaneous, then you are saying that two clocks at those locations can be synchronized by those events.
When you say that the light will hit the two sides of your mirror at the same time, you are implying that two synchronized clocks would have the same reading when the light hits them there. Saying that the lights "hit the two sides of your mirror at the same time" has all the same problems that clock synchronization has.

It will require two distinct measurements. It is up to you whether you want to call one of them callibration. The result will be a measurement of the round trip time.

When you say that the light will hit the two sides of your mirror at the same time, you are implying that two synchronized clocks would have the same reading when the light hits them there.

I have moved away from the mirror in post 22, replacing it by a mechanical means of stopping both clocks 'supposedly simultaneously'.

Now if the rotating shaft is not suited, then we could substitute for a linear motion, having the same step motor pushing a flat surface holding the two blades until they reach each clock's photo cells, stopping them.

This is just a thought experiment, implying that both blade's edges are at the same distance, thus entering the photo cells at the same time. You might say, "well, how can you make sure they are at the same time ?", that's just it, it's a thought experiment, so in that thought experiment they are...

I mean, can't we have some degree of accuracy about the edges being aligned the best they could be, and have some degree of accuracy as to how the flat surface moving towards the photo cells in a steady way ?

Anyway...

Now if the rotating shaft is not suited, then we could substitute for a linear motion, having the same step motor pushing a flat surface holding the two blades until they reach each clock's photo cells, stopping them.
You are assuming that these devices are built out of a perfectly rigid material, such that if one part of an object is displaced all other parts of the object will be be simultaneously displaced by the same amount - that's the definition of an ideal rigid body.
However, there is no such thing as an ideal rigid material; if there were we could send a faster than light signal simply by pushing on one end of a long rigid rod and expecting the other end to move as soon as we do. In practice when we displace one part of an object there is a time lag before the impulse propagates via the electromagnetic forces between the atoms to the rest of the object; that time lag will only be the same in both directions if the speed of light is the same in both directions. Thus we cannot use any mechanical device to stop the two spatially separated photocells "at the same time" - we've just found another way of assuming what we've set out to prove.

Lord Jestocost
All I can say here is, please close this thread...

OWSOL

that time lag will only be the same in both directions if the speed of light is the same in both directions.
Ok, maybe not yet...

Nugatory, what do you mean by "in both directions", the flat surface is moving towards both clocks in only one direction.

Thank you