# Can someone travelling at c race a photon?

1. Aug 12, 2013

### QuestionMarks

In trying to understand relativity, I once read a statement that even travelling at the speed of light, an emitted photon travelling in your direction would still move away from you at the speed of light.

This confuses me as I have a hard time correlating it to a real scenario. Say "The Flash" (moves at c) was at a starting line with a flashlight. Could he not race the photons emitted from the flashlight? But what if The Flash was carrying a flashlight while he ran and then turned it on; is this when the photons would move away from him at the speed of light even though he is travelling that speed?

If so, this seems even more mind-boggling to me than I had originally understood relativity to be. I know it's often said that science doesn't like to address "why issues" per say, but is there any philosophical context perhaps that makes this necessity more intuitive if I'm right here?

2. Aug 12, 2013

### Staff: Mentor

Nothing with mass can move at c.

However, if you were moving at .99999 c wrt me you would still measure light to be traveling at c wrt you.

Last edited: Aug 12, 2013
3. Aug 12, 2013

### QuestionMarks

Then suppose something with no mass distinct from a photon, or another photon, or even just a hypothetical situation.

4. Aug 12, 2013

### cmcraes

The problem here is youre assuming some observer has the ability to travel at the speed of light. This is impossible because as you approach c, Your length would approach 0, Your perceived time would slow down to almost as if time were not flowing, and your mass would approach infinity. These consequences make it impossible to travel at c (unless you have an infinite source of energy). So in every reference frame light will travel at c, no matter your speed.

5. Aug 12, 2013

### cmcraes

Ok well hypothetically, A massless observer would have a pretty boring view. From what I can assume, Because the observer is traveling at c, to him, it would seem as though it took him no time to travel from one point to another. All of space would appear as a single point, so you probably wouldn't see much at all.

6. Aug 12, 2013

### Staff: Mentor

7. Aug 12, 2013

### Staff: Mentor

The problem is that you can't make a change to the laws of the universe and then how the laws of the universe will behave. It's a contradiction/unanswerable. At that point, you can just make it up as you go along and it won't have any relation to the way the real universe works.

8. Aug 12, 2013

### QuestionMarks

I guess Dale's edit answers largely my question now. Does it apply to both situations though (A- the flashlight emits at the same time from the start line, and B- the flashlight is carried with the flash and turned on after running)?

9. Aug 13, 2013

### ghwellsjr

Yes, both.

Realize that you cannot observe the propagation of a flash of light unless it reflects off something and returns to you. So the logical way to measure the speed of light is to put a mirror out in front of you, start a stopwatch when you turn on your flashlight and stop it when you see the reflection of the light. Of course, this will happen so fast that you can't depend on your own reaction but nowadays we can build electronic circuits to accurately make the measurement for us.

So let's say "The Flash" builds an apparatus with a light source and light detector at one end and a mirror seven feet away at the other end. A very fast circuit starts a timer when the light source is turned on and 14 nanoseconds later the detector senses the reflection and stops the timer. Since light travels at 1 foot per nanosecond and it takes 7 nanoseconds to get to the mirror and another 7 nanoseconds for the reflection to get back we can see that his measurement comes out right.

Here is a diagram that depicts the measurement:

"The Flash" is depicted as the thick blue line and his mirror as the thick red line. At the Coordinate Time of 0 nsecs the thin blue flash of light is emitted and travels at 1 foot/nsec to the mirror, reflecting off of it as shown by the thin red line at the Coordinate Time of 7 nsecs and returning to "The Flash" at the Coordinate Time of 14 nsecs. The blue dots show 1 nsec increments of the timer counting a total of 14 increments. Does this all make sense to you?

In order to see how Special Relativity depicts the situation when "The Flash" is traveling at a very high speed (I picked 96% of the speed of light) we use the Lorentz Transformation. The net result of this is shown in this diagram:

Now you can see that "The Flash" is chasing the thin blue flash of light. He's right behind it for a distance of 47 feet but then it hits the mirror and almost immediately returns to him as the short thin red line. You will note that his time is running slower than it was before--this is Time Dilation and you will not that the mirror is closer to him--this is Length Contraction. The net result is that his measurement comes out the same. Does this make sense?

Note that it won't make any difference if the light was started by "The Flash" with a flashlight carried with him or if the light came from an external source that is stationary as long as it can start his timer when it passes by him on the way to his mirror.

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Last edited: Aug 13, 2013
10. Aug 13, 2013

### Staff: Mentor

Yes. The difference between those two will be the Doppler shifted frequencies, but the speeds will be the same.

11. Aug 14, 2013

### m4r35n357

Actually, with a big enough head start and constant aceleration you can theoretically outrun a photon forever, without ever going faster than light. This is probably the most readable reference that I know of: http://math.ucr.edu/home/baez/physics/Relativity/SR/rocket.html [Broken]

Last edited by a moderator: May 6, 2017
12. Aug 14, 2013

### QuestionMarks

Im not sure if I was able to draw the outrunning conclusion, but the rest makes sense (so thanks everyone, and for the graphs). Seems I was underestimating relativity a bit heh

13. Aug 15, 2013

### m4r35n357

14. Aug 15, 2013

### pervect

Staff Emeritus
If you're looking for a textbook reference for the details of accelerated motion, MTW's gravitation has it. Otherwise, I think the sci.physics.faq reference is a good one, I'm not quite sure what problem the OP had with it. If it's just that it was a bit advanced, going to the textbook reference won't help any - but if there was a need for more details and rigor, the textbook reference might be helpful.

MTW's treatment of the problem uses tensor notation as I recall, however.