# A beam of light compared to bullet in gun

1. Aug 20, 2010

### freshnfree

If a train goes past an observer at 100km/hour and someone on the train fires a bullet from a gun in the direction the train is going at 700km/hour, then relative to an observer, that bullet will go past at 800km/hour. Einstein made a statement of the type that if a person on the train holds a torch they will see the light beam at the "speed of light" and an observer on the ground will also see that light beam at "the speed of light" ie the speed of light is always constant from any frame of reference. He then proceeded to make a theory which included time speeding up or slowing down to explain why the speed of light is always constant for any frame of reference. But that was because he thought that the light beam should behave like the bullet in that you could add the speed of the train to its speed and because you couldn't add the speed of the train to the speed of light, he made a fairly complex theory to compensate for it not behaving like the bullet.
Yet the light beam has many differences to the bullet. It is instantaneously produced from the torch or flashlight. The bullet is carried onto the train. The light beam is instantaneously produced. Is the light beam actually "on" the train. Do the photons of the light beam at any time rest on any surface of any thing which is on the train or do they simply emanate from the torch? If the photons are not "on" the train, they will not carry the velocity of the train. Therefore you would expect the speed of light to be the same for any frame of reference without having to do any compensating for it. If this logic is not correct, please let me know where you think I have gone wrong.

2. Aug 20, 2010

### Passionflower

Not exactly 800 km/hour but less by an extremely small amount.

3. Aug 20, 2010

### Janus

Staff Emeritus
Let's be clear about what is meant by "the speed of light is a constant". It means that the speed of light as measured by you, relative to you, always is the same value.

Thus if I am sitting in the middle of the train and fire a light pulse towards the ends, since I am halfway between the ends and the light travels at the same speed in both directions, according to me, the light pulses hit the ends at the same time.

However, according to someone on the embankment, the light travels at the same speed in both directions relative to himself. Thus one end of the train is running towards the light and the other is running away from it. For this person one pulse hits one end of the train before the other hits its end of the train.

You end up with observers watching the same events and determining that they occurred at different times. The measurement of time differs between relative moving observers.

Besides that, it is a bit of a moot point, as the time dilation predicted by the theory has been confirmed by experiment.

4. Aug 20, 2010

### freshnfree

I have searched the web for experiments on time dilation and they seem to be pretty thin on the ground. The one most mentioned is one done in 1971. As is commonly known, scientific method involves experiments which are repeatable. And to be truly methodical, experiments should be done many times to account for instrument error, human judgement, environment variables and many other factors that can play a part in an experiment's success. I am surprised that for such a famous theory, which involves time slowing down, a powerful statement, there seem to be so few found on the net. Also, this theory seems to be have been commonly accepted before any experiments were ever done, which when the experiments were finally done, could introduce bias, as the expermenters may not have wished to go against an already commonly held belief.

5. Aug 20, 2010

### Janus

Staff Emeritus
You couldn't have searched very thoroughly. Relativistic time dilation is verified daily with particle accelerator experiments, and by the fact that the GPS system has to be designed with it in mind in order to work properly.

6. Aug 20, 2010

### netheril96

And GPS even involves general relativity.

7. Aug 20, 2010

### freshnfree

Does any one have any links from reputable sources where experiments have been done and repeated showing exact results which prove time dilation occurs. Also, are there links from reputable sources which show GPS uses time dilation calculations.

8. Aug 20, 2010

### matheinste

Check out trasnverse Doppler effect, which is often regarded as a demonstration of time dilation predicted by SR.

Matheinste

9. Aug 20, 2010

### Staff: Mentor

What type of source, specifically, would satisfy your concerns?

10. Aug 20, 2010

### JesseM

A bunch of notable experiments are listed here. A simple experiment demonstrating gravitational time dilation can be seen here.
A basic summary of how GPS works can be read here, more detailed explanations http://relativity.livingreviews.org/Articles/lrr-2003-1/ [Broken] (pdf version here) and here.

Last edited by a moderator: May 4, 2017
11. Aug 21, 2010

### yuiop

You can look at the whole question in terms of velocities using relativistic velocity addition which treats massive and massless particles equally and so makes no special distinction between bullets and photons per se.

To analyse the velocity of a particle that is not parallel to the relative motion of two frames, it is convenient to break down the velocity of the particle into components that are parallel and transverse to the motion. Assume two frames A and B that have relative motion in the x direction and their axes are parallel to each other.

Using notation based on a https://www.physicsforums.com/showpost.php?p=2829317&postcount=40" and units of c=1, the addition of the parallel components is given by :

$$X_{CA} = \frac{X_{CB} + X_{BA}}{1+X_{CB}X_{BA}}$$

where the symbol X means velocity measured in the X direction and $X_{CA}$ means the velocity of particle C according to observer A, $X_{CB}$ means the velocity of particle C according to observer B and $X_{BA}$ means the velocity of observer B according to observer A.

The addition of the components orthogonal to the motion in the X,Y plane is given by:

$$Y_{CA} = \frac{Y_{CB} \sqrt{1-X_{BA}}}{1+X_{CB}X_{BA}}$$

where $Y_{CA}$ means the Y component of the velocity of particle C as measured by observer A and so on.

Now in a practical example, let us say that observer B measures the velocity of a photon to be 1.0c in the Y direction and A measures B to moving at 0.8c in the X direction. The X component of the photons velocity is 0.8c according to observer A and the Y component of the photons velocity is 0.6c according to observer A. The total velocity of the photon according to observer A, without regard to direction (i.e. the speed of the photon) is sqrt(0.8^2+0.6^2)c = 1.0c so both observers A and B still agree that the speed of the photon is 1.0c although they disagree on the direction of the photon's velocity vector, from their different points of view. The relativistic velocity equations are formulated with an assumption that momentum is conserved so any results obtained from using the equations should be consistent with momentum conservation by definition.

For completeness, when considering 3D motion, the Z velocity component is given by:

$$Z_{CA} = \frac{Z_{CB} \sqrt{1-X_{BA}}}{1+X_{CB}X_{BA}}$$

and the total speed $V_{CA} = (X_{CA},Y_{CA},Z_{CA})$ of a particle C according to observer A, which has speed $V_{CB} = (X_{CB},Y_{CB},Z_{CB})$ according to observer B, can be calculated using:

$$V_{CA} = \left| \, \sqrt{\frac{(X_{CB}+X_{BA})^2 +Y_{CB}^2(1-X_{BA}^2) + Z_{CB}^2(1-X_{BA}^2)}{(1-X_{CB}X_{BA})^2} \, \right|$$

Last edited by a moderator: Apr 25, 2017
12. Aug 21, 2010

### freshnfree

The experiments which prove that time dilation occurs deal with time differences in the order of nanoseconds, ie billionths of a second. For the experiments to be accurate the two atomic clocks would have to be synchronised to within nanoseconds of each other and proven to be synchronised to within nanoseconds. Also when the time was read from each of them, once they returned from their journey, it would have to be read from them at exactly the same nanosecond or in the realm thereof. Does anyone know how they managed to achieve this?

13. Aug 21, 2010

### JesseM

Not necessarily, did you see the "measurement of particle lifetimes" section here? See for example the discussion of muon decay on p. 41-42 here--the muon has a lifetime of about 2 microseconds in its rest frame, but this is extended considerably for muons created by particle collisions in the upper atmosphere, which have a typical speed of around 0.998c relative to the Earth.
I don't know the details but I'd imagine the clocks would be brought together and one would send a timestamp with each oscillation that's used to set the time for the oscillations of the other. In any case, they're apparently pretty accurate, this book mentions that the atomic clocks on GPS satellites "have a stability of about 1 part in 10^13 over a period of 1 day", or an error of about 9 nanoseconds per day.

14. Aug 21, 2010

### Staff: Mentor

See the sticky thread at the top of this very forum, titled "FAQ: Experimental Basis of Special Relativity".

15. Aug 22, 2010

### freshnfree

I have been given links which are not really giving me the information I am asking. A father taking his 3 kids up a mountain with some atomic clocks is not my idea of an experiment which will convince me that time does indeed move more slowly in certain situations. Einstein's theory was widely believed for any experimentation was done. Already scientific method was not being followed. For any experiment to be taken seriously, all the measurements, all the calculations, all the machinery, the exact method in which the measurements were taken have to be available with the results of the experiments, otherwise the experiment has no credibility. The experiment should be repeated at least several times. I went to a link about a book about GPS. I would then have to buy the book to read where it talks about time dilation. I have yet to see an experiment which looks even remotely credible and which contains all the details of that experiment. Anyone can say that they did an experiment that proves time moves more slowly. Yes, I just walked up the mountain out the back of my place and set up an atomic clock. I left it there a coupla days, came back down with it, drew a couple of graphs and hey presto, I just proved that time does move more slowly.

16. Aug 22, 2010

### matheinste

Isn't it strange, that for all the misguided scientists performing inaccurate and meaningless experiments, we were actually able to build a thing like the LHC. It seems such a waste of money, and maybe even dangerous, if the science upon which it is based relies on such sloppy experimentation.

What experimenters do is more or less exactly what you say they should do. They have to do this if they want their work to be taken seriously. Its the usual scientific method.

Matheinste.

17. Aug 22, 2010

### Staff: Mentor

You've been pointed to a FAQ that contains references to scientific journal articles about tests of time dilation. These generally give details of the experimental procedures. Some of these articles may be available somewhere on the Web, otherwise you can find them in university libraries or have them sent to your library via interlibrary loan.