What Would Light Look Like If Train Moved at > Speed of Light?

[sigr]

I am reading up on the special theory of relativity, and watched a video. In the video we have a train moving at ½ c towards a station, where an observer is waiting. The train's headlamp is on. How would the lamp's light appear to the observer?

I was thinking that it¨'d appear to the observer as there were something funny with the light, since the train moves at that speed. Why? Because light are photons, and when the train moves at half the speed of light towards our observer, such photons would come more frequently to the observer (the observer would be hit by more photons per second), and thus the light coming from a train moving at half the speed of light would appear different to the observer?

Am I wrong here?

Taking this a step further. Let's say it was possible to break the rules of physics and our train would move faster than the speed of light, then the train would "mop-up" the photons emitted from the headlamp, right?

 

[Janus]

The effect you are describing is the Doppler effect. You would see that light at a higher frequency than that emitted by the train. At 0.5c, you would see the light shifted at factor of 1.732 . It would be "blue-shifted". ( light at the red end of the visible spectrum would shift towards the blue end.)
We use this effect to measure how fast distance objects in space are moving towards or away from us. It is also the principle that Police radar uses to measure the speed of your car. ( the radar beam's frequency is effected by bouncing off your moving car. The radar gun compares this shift to the emitted frequency to determine how fast you are driving.)

As for your "step further" question. You can't really answer it without first determining "how" you broke the rules of physics. By our present understanding, the speed of light is invariant. Meaning both you and the train would measure it as moving at c relative to themselves. In other words, while in your first example, yo would measure the photons as having a speed of c relative to you and 0.5c with respect to the train, the train would measure them as having a speed of c relative to it and 1.5 c with respect to you.

You can see as where this would create a problem if you assume that you could measure the train as having a speed greater than c relative to you. You would indeed see the photons being "mopped up" without ever leaving the train. But the train would still measure the photons as streaming away ahead of it at c. You would have a paradox where the light both did and did not leave the train.

Thus For the train to be able to exceed c, you would need a whole new model for light behavior to describe what would happen.

Essentially, when you try to envision a scenario where you are allowed to break the laws of physics, you also break the "tools" needed to tell you what would happen in that scenario. You can't use the same rules that says " x can't happen" to tell you what would occur if x could happen.

 

[vanhees71]

First of all you should understand that photons are not what you think they are. They are not little bullet-like objects, and also it's way simpler and more to the point to think of light in terms of electromagnetic waves. If needed you can always do QED, which is the correct quantum description of light, and there photons are just a one-quantum Fock state, but as I said, you don't need this to answer your question.

All you need is that light is an electromagnetic wave. Then there is a wave four-vector $k=(\omega/c,\vec{k})$, which is light-like, $k_{\mu} k^{\mu}=0$.

Now for simplicity let the train move in positive $x$ direction, and then the light of the train's headlight is going (approximately if the train is far away) also in positive $x$ direction. Thus you have $k=(\omega/c,\omega/c,0,0)$. The four-velocity of the train $u=\gamma (1,\beta,0,0)$, where $\beta=v/c$. Now you can calculate easily the freqency of the light in the train's rest frame,
$$\omega_0=c u \cdot k=\gamma \omega (1-\beta)=\sqrt{\frac{(1-\beta)^2}{1-\beta^2}} \omega = \sqrt{\frac{1-\beta}{1+\beta}} \omega$$
or
$$\omega = \sqrt{\frac{1+\beta}{1-\beta}} \omega_0,$$
i.e., the light is blue-shifted by a factor $\sqrt{3}$ (for $\beta=1/2$).

 

[PeroK]

I am reading up on the special theory of relativity, and watched a video. In the video we have a train moving at ½ c towards a station, where an observer is waiting. The train's headlamp is on. How would the lamp's light appear to the observer?

I was thinking that it¨'d appear to the observer as there were something funny with the light, since the train moves at that speed. Why? Because light are photons, and when the train moves at half the speed of light towards our observer, such photons would come more frequently to the observer (the observer would be hit by more photons per second), and thus the light coming from a train moving at half the speed of light would appear different to the observer?

Am I wrong here?

Taking this a step further. Let's say it was possible to break the rules of physics and our train would move faster than the speed of light, then the train would "mop-up" the photons emitted from the headlamp, right?

Both the energy and intensity of the light would increase.

You can't take it a step further. That hypothesis leads to nonsense rather than physics.

 

[pervect]

I am reading up on the special theory of relativity, and watched a video. In the video we have a train moving at ½ c towards a station, where an observer is waiting. The train's headlamp is on. How would the lamp's light appear to the observer?

I was thinking that it¨'d appear to the observer as there were something funny with the light, since the train moves at that speed. Why? Because light are photons, and when the train moves at half the speed of light towards our observer, such photons would come more frequently to the observer (the observer would be hit by more photons per second), and thus the light coming from a train moving at half the speed of light would appear different to the observer?

Am I wrong here?

I believe you are trying to describe the effect known as "relativistic beaming".

https://en.wikipedia.org/w/index.php?title=Relativistic_beaming&oldid=921182258

Relativistic beaming (also known as Doppler beaming, Doppler boosting, or the headlight effect) is the process by which relativistic effects modify the apparent luminosity of emitting matter that is moving at speeds close to the speed of light.

The classical view of the "greater number of photons per second" that you describe is "greater luminosity", which is just what relativistic beaming describes

"looking funny" is a bit vague, we can say more precisely that for the headlight of an incoming train, the light is doppler shifted to a higher frequency, and that additionally the "relativistic beaming" effect makes the headlights more intense.

You didn't ask about the frequency shifting effect - I thought I'd mention its existence, but the effect you seem to be talking about is not related to the frequency shift, but to the change in intensity.

While photons can be tricky in some circumstances, because they are quantum rather than classical particles, in this particular case I don't think it matters much.

Taking this a step further. Let's say it was possible to break the rules of physics and our train would move faster than the speed of light,

Let's not say that, because applying the laws of physics to answer questions about said laws while simultaneously assuming that one can break the laws of physics leads to logical contradictions.

This is a general feature of logic - if one makes logically inconsistent assumptions, one reaches absurd conclusions. This is the basis of the mathematical technique called "reducto ad absurdum", when one reaches an absurd conclusion, one knows that one has made inconsistent logical assumptions. You're setting yourself up to reach absurd conclusions by assuming that you can break the laws of physics and apply them at the same time.

 

[sigr]

Whoa, that was a lot to take in for a noob. But thanks! Appreciated! The gist of it is that the bullet model of the photon is wrong, I guess.

I believe you are trying to describe the effect known as "relativistic beaming".

https://en.wikipedia.org/w/index.php?title=Relativistic_beaming&oldid=921182258The classical view of the "greater number of photons per second" that you describe is "greater luminosity", which is just what relativistic beaming describes

"looking funny" is a bit vague, we can say more precisely that for the headlight of an incoming train, the light is doppler shifted to a higher frequency, and that additionally the "relativistic beaming" effect makes the headlights more intense.

You didn't ask about the frequency shifting effect - I thought I'd mention its existence, but the effect you seem to be talking about is not related to the frequency shift, but to the change in intensity.

While photons can be tricky in some circumstances, because they are quantum rather than classical particles, in this particular case I don't think it matters much.

Yes! Relativistic beaming! Sounds like we're onto something!

What do you think of this scenario. Is it somewhat correct, with regards to number of photons? Here I am still using the bullet model of a photon.

We have two trains lost in space, 100 light-years from Earth. Both trains have their headlamps on, pointed at us, and these lamps stay on for 100 years. One of the trains stays put, while the other moves towards Earth at a speed infinitesimally slower than light.

Going with the bullet model of the photon, I'd guess this would happen.

• Train that stays put, lamp has 500 lumen. For a hundred years it would be pitch-black when we'd look for the headlamp in the night sky, but after a hundred years, we'd get 500 lumen, which would last for a hundred years before it'd be pitch-black again. How many photons would that be?
  • One lumen is a quadrillion photons a second.
  • Our lamp's strength is 500 lumens.
  • A hundred years has some 3,153,600,000 seconds.
  • Multiply it all, and Earth would be hit by 1.568e+27 photons, in the span of 100 years.
• Train that moves close to c, lamp has 500 lumens. Our train travels at a speed where it'd close the distance of 100 light-years in just a single second more than the emitted photons. So, if we'd look at the night sky from Earth, we'd see nothing for 100 years. But in a brief second, we'd see a flash, before it'd be dark again. How many photons would that be?
  • 1.568e+27 photons, but in 1 second.
  • That would be tantamount to a lamp of 157,680,00,000 lumen, shining for 1 second.

Are those calculations of numbers of photons horribly wrong? I haven't taken into account a blue shift. Not at all. Which I guess would bring down the total number of photons in the second case, as photons from blue-shifted light have more energy.

And naturally I've assumed that all of the light hits Earth.

First of all you should understand that photons are not what you think they are. They are not little bullet-like objects, and also it's way simpler and more to the point to think of light in terms of electromagnetic waves.

Way simpler? Sounds enticing! (Big smiles)

Yes, I guess it's time for me to abandon the bullet model. I know it's faulty, but at least it gave me the notion of photon accretion when the light source moves towards you, which I guess is right. But not color change, which is due to changes in wave length, giving each photon more energy - if I'm right.

Going by the correct model of the photon, the wave model, would it be possible to guesstimate the number of photons that'd hit Earth by the single second flash from the second train? I'm guessing the number would be lower due to the blue shift. That the blue shift'd muddle things.

 

[jbriggs444]

Train that moves close to c, lamp has 500 lumens. Our train travels at a speed where it'd close the distance of 100 light-years in just a single second more than the emitted photons. So, if we'd look at the night sky from Earth, we'd see nothing for 100 years. But in a brief second, we'd see a flash, before it'd be dark again. How many photons would that be?

• 1.568e+27 photons, but in 1 second.
• That would be tantamount to a lamp of 157,680,00,000 lumen, shining for 1 second.

You've neglected relativistic time dilation. The train's clocks and lamps are running slow and only about an hour and a half's worth of light is emitted.

From the moving train's point of view, the trip took only an hour and a half and covered 1.5 light-hours of length-contracted distance.

 

[vanhees71]

To answer the question about intensity you have to Lorentz transform the energy-momentum tensor of the em. field!

 

[sigr]

You've neglected relativistic time dilation. The train's clocks and lamps are running slow and only about an hour and a half's worth of light is emitted.

From the moving train's point of view, the trip took only an hour and a half and covered 1.5 light-hours of length-contracted distance.

Whoa. I'm falling further down the rabbit hole! This is some fascinating stuff. I see I've got a lot of ground to cover, a lot of concepts to get familiar with. To all of you: thanks a lot for awesome answers, in the original sense of the word.

 

[pervect]

Whoa, that was a lot to take in for a noob. But thanks! Appreciated! The gist of it is that the bullet model of the photon is wrong, I guess.

Yes! Relativistic beaming! Sounds like we're onto something!

What do you think of this scenario.

I'd rather write my own scenario. I'll start by replacing "lumens", which are weighted to the sensitivity of the human eye, with a measure of power, a measure of the energy/unit time that is not weighted according to the spectral sensitivity of the human eye.

https://en.wikipedia.org/w/index.php?title=Lumen_(unit)&oldid=917091375 has some details on the difference. Power is sometimes called "radiant flux" in this context, as wiki mentions, but power seems easier to me to write. Lumens are a measure of luminous flux, and are weighted towards human visual sensitivity, while radiant flux (or just power) is not weighted in this manner.

Suppose we have a monochromatic (single frequency) laster beam, with a 1 meter squared cross section, that has a total power of 100 watts in the rest frame of the laser. A real beam would have to diffract some, but we'll assume that diffraction is negligible.

We can accelerate the laser and keep the target stationary, or keep the laser stationary and accelerate the target. By the principle of relativity, the answer of what happens to the power of the laser beam as measured by the target won't matter. It's probably easier to imagine that we accelerate the laser beam, because we'll be doing all our measurements in the frame of the target.

Let's make the relative velocity between the laser beam and the target v=.866c, so that the gamma factor, the time dilation factor , is 2, where $\gamma = 1 / \sqrt{1-\beta^2}$ and $\beta = v/c$.

We will also assume that the target is moving directly towards or away from the laser and is oriented perpendicularly. There is no length contraction in the perpendicular direction, so the cross section area of the beam doesn't change. So the total power in the beam scales the same as the power/unit area.

Then the laser beam that had 100 watts of power will have 400 wats of power as measured by the target, if the target is moving towards the laser beam, and 25 watts of power, if it is moving away. There is a 4:1 factor in power when the gamma factor is 2.

Let's look at the 400 watt case in terms of "photons".

The frequency of the laser beam is doubled from it's rest frequency in the frame of the moving target. By the relation $E = h \nu$, the energy in each photon is doubled.

The photons also arrive at twice the rate. So in a given amount of time, t twice as many photons arrive in the frame of the moving target.

The result is 4 times as much energy / unit time, i.e. 4 times the power. I'm using SI units, so the approprirate unit is the watt.

The general relation is that the total power scales as $\gamma^2$, as does the power / unit area since the area doesn't change.

This can be described classically, without photons, but it's probably actually easier to talk about it in terms of photons, in this particular case.

 

[Keith_McClary]

Cute Carl Sagan video on "what if the speed of light were slower". (I've seen others on youtube, but can't find them.)

 

[Mister T]

Cute Carl Sagan video on "what if the speed of light were slower". (I've seen others on youtube, but can't find them.)

Search YouTube for Mr. Tomkins in Wonderland.

 

[pervect]

Cute Carl Sagan video on "what if the speed of light were slower". (I've seen others on youtube, but can't find them.)

I think this is starting to drift off the topic of the Original Poster. If there's some interest in Sagan's video, or Mr. Tompkins, it might be a good topic for a different thread.