# Radar echo and clock synchronization

## Main Question or Discussion Point

It is well known that the radar echo (police radar) establishes a relationship between the period T(e) at which a stationary observer emits successive light signals and the period T(r) at which he receives them back after reflection on an object that moves with constant speed V. Both time intervals are measured as a difference between the readings of the observer's wrist watch and so IMHO no clock synchronization is involved. If the moving object is receeding the two periods are related by
T(r)/T(e)=(1+V/c)/(1-V/c).
My question is: Does the measurement of the speed V involve clock synchronization?

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It is well known that the radar echo (police radar) establishes a relationship between the period T(e) at which a stationary observer emits successive light signals and the period T(r) at which he receives them back after reflection on an object that moves with constant speed V. Both time intervals are measured as a difference between the readings of the observer's wrist watch and so IMHO no clock synchronization is involved. If the moving object is receeding the two periods are related by
T(r)/T(e)=(1+V/c)/(1-V/c).
My question is: Does the measurement of the speed V involve clock synchronization?
You'll have to answer a few questions:

1. Is the above formula related to SR? Yes or No?
2. How was the formula derived?

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Meir Achuz
Homework Helper
Gold Member
How could it involve clock synchronization if you don't tell the cop the time of day? Who can he synchronize with?

russ_watters
Mentor
If there is only one clock, what would you synchronize it with?

pervect
Staff Emeritus
It is well known that the radar echo (police radar) establishes a relationship between the period T(e) at which a stationary observer emits successive light signals and the period T(r) at which he receives them back after reflection on an object that moves with constant speed V. Both time intervals are measured as a difference between the readings of the observer's wrist watch and so IMHO no clock synchronization is involved. If the moving object is receeding the two periods are related by
T(r)/T(e)=(1+V/c)/(1-V/c).
My question is: Does the measurement of the speed V involve clock synchronization?
This procedure will give the speed of the car with a fair (or isotropic) clock synchronization. This is the sort of clock synchronization that makes the speed of light equal to 'c' in all directions.

Usually one would try and demonstrate this result by assuming isotropy, and then showing in detail how the procedure measures speed.

This procedure will give the speed of the car with a fair (or isotropic) clock synchronization. This is the sort of clock synchronization that makes the speed of light equal to 'c' in all directions.

Usually one would try and demonstrate this result by assuming isotropy, and then showing in detail how the procedure measures speed.
Thanks. Asher Peres Am.J.Phys. 55, 516 1987 and Peter Kenny Phys.Educ, 41, 334 (2006) start the derivation of the time dilation formula with an experiment known as radar echo (police radar) establishing a relationship between the time T(e) at which a stationary observer emits a light signal towards a moving mirror and the time T(r) at which the reflected light signal is received back. It is considered that at T=0 the mirror was in front of the stationary observer and that the clock comoving with the mirror was in front of the source reads a zero time (T'=0). Because the time intervals
T(e)-0 and T(r)-0 are measured as a difference between the readings of the same clock. Asher Peres and I aggree with him,concludes that the radar echo experiment does not involve any synchronization convention The formula which accounts for the radar echo effect contains the relative velocity V. I understand from your answer, with which I aggree, that the measurement of V involves clock syncronization in the the stationary reference frame but not in the rest frame of the mirror, if the clock comoving with it reads zero when it is located in front of the source.
That fact is not allways mentioned by the Authors I know so far.
For the same reasons we can ask: when becomes clock synchronization invollved in Einstein's derivation of the Lorentz transformations: when he measures the relative velocity of the involved reference frames or when he derives the invariance of the interval? I hope that nobody will accuse me that I do not respect my TEACHER!
Am I right? Your confirmation is essential for me in the preparation of a book entitled "Special relativity with human face". I think in special relativity nobody is perfect. :rofl:
That answer is, with thanks, for all who have oppened my thread.

radar echo, time dilation, clock synchronization.

If there is only one clock, what would you synchronize it with?
Good question. Even if per se the radar echo experiment does not involve clock synchronization the measurement of V requires. That is a fact not allways mentioned in the problem of the radar echo or of the time dilation. I intend to mention that fact somewhere and I need a confirmation. That is why we are on the Forum.:rofl:

-when he measures the relative velocity of the involved reference frames
He doesn't do any of that.

-or when he derives the invariance of the interval? .

Neither.Please look up his paper, the clock synchronization condition is turned into a partial differential equation in t via using Taylor expamsion. The solution of the equation produces the Lorenz transforms. As such, the Einstein clock synchronization is essential in the derivation of the Lorentz transforms. (at least in his derivation).

The invariance of the spacetime interval is a consequence of the Lorentz transforms.
The Lorentz transforms are a consequence of Einstein's clock synchronization.

All of the above is quite plain in his paper.

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How could it involve clock synchronization if you don't tell the cop the time of day? Who can he synchronize with?

You'll have to answer a few questions:

1. Is the above formula related to SR? Yes or No?
2. How was the formula derived?

It is well known that the radar echo (police radar) establishes a relationship between the period T(e) at which a stationary observer emits successive light signals and the period T(r) at which he receives them back after reflection on an object that moves with constant speed V. Both time intervals are measured as a difference between the readings of the observer's wrist watch and so IMHO no clock synchronization is involved. If the moving object is receeding the two periods are related by
T(r)/T(e)=(1+V/c)/(1-V/c).
My question is: Does the measurement of the speed V involve clock synchronization?
I rephrase my question. If the equation presented above and which accounts for the radar echo then it leads to V the velocity of the mirror which reflects the radar signal. Defined as
V=proper length/coordinate time interval the measurement of V requires the synchronization of the clocks in the stationary reference frame. Is tghere a way out from the labirinth. I am not able to find it.

Jorrie
Gold Member

V=proper length/coordinate time interval the measurement of V requires the synchronization of the clocks in the stationary reference frame. Is there a way out from the labirinth. I am not able to find it.
Hi Bernard, have you considered this method to (perhaps) get out of the 'labyrinth'?

It seems that your question is how the speed V, as obtained by the radar, can be verified directly without relying on any clock synchronization. I assume you are talking about flat spacetime with two inertial observers moving past each other with relative velocity V.

Let both observers agree to use rulers to measure out identical distance grids with uniform spacing in their respective inertial frames and mark their grids physically and visibly. Each observer can now use his/her own clock to time the rate (or period) at which the other's grid markers flash past. Knowing the proper separation between markers, each observer can calculate their relative speed without synchronizing any clocks.

I'm not sure if this doesn't just create another 'labyrinth'…

Hi Bernard, have you considered this method to (perhaps) get out of the 'labyrinth'?

It seems that your question is how the speed V, as obtained by the radar, can be verified directly without relying on any clock synchronization. I assume you are talking about flat spacetime with two inertial observers moving past each other with relative velocity V.

Let both observers agree to use rulers to measure out identical distance grids with uniform spacing in their respective inertial frames and mark their grids physically and visibly. Each observer can now use his/her own clock to time the rate (or period) at which the other's grid markers flash past. Knowing the proper separation between markers, each observer can calculate their relative speed without synchronizing any clocks.

I'm not sure if this doesn't just create another 'labyrinth'…
Thanks. That is the way in which I like discussions on the Forum. Let me rephrase your answer, which I intend to include it in a paper.
In the equation T(r)=T(e)[1+V/c]/[1-V/c} the measurement of the two time intervals does not involve clock synchronization. The measurement of V defined as V=proper length/coordinate time interval requires it. We can define the proper velocity U=proper length/proper time interval, the measurement of which does not require clock synchronization. The two velocities are related by
V=U/sqrt(1-UU/cc) being equal to each other at small velocities, I hope I am now out from the "labyrinth" with your help of course. If not the discussion is olpen. I think we should mention all that when we teach the radar echo and the Doppler shift