Light Speed: Fixed... or Relative? Exploring Einstein's Relativity

Einstein once imagined a brilliant thought experiment. He pictured a moving train, with a man inside, and a stationary platform, with another man on it. As the train passes right next to the platform, two lighting bolts simultaneously strike both ends of the train. Let's dub these two events as "event A" and "event B". Event A is the name of the lighting striking the rear end of the train, and Even B is the name of the lighting striking the front end.

According to Special Relativity, Event A and Event B will be observed as simultaneous events by the man on the platform. Since he doesn't move, the light of both events reaches the man at the same time.

But as for the man on the moving train, he won't be observing the two events as simultaneous. The train is moving forward. This means it'll catch up with the light from Event B very quickly, even before this same light reaches the stationary observer on the platform. Additionally, as the train will be moving away from Event A, it'll take additional time for this Event A's light to reach the man on the train, making the two events seem non-simultaneous.



This thought experiment is heavily quoted in Special Relativity textbooks. Yet, as much as it is incredibly logical, this thought experiments predicts something weird. An anomaly. The anomaly is located within the moving frame (the blue guy in the picture). It seems that for this thought experiment to work, light's speed relative to the observer is changed. Light from Event B reaches the observer at a relative speed well ABOVE c, and light from Event A travels toward the observer at a very slow relative speed, well BELOW c.



In the stationary's inertial frame, the speed of light (relative to the green guy) is at exactly c, but this stops being the case in the moving inertial frame (relative to the blue guy). Remember that the moving observer frame can be considered an inertial frame too, in such a way that this observer may not be aware of other frames, even to the point of assuming that HE is the stationary frame. In this next picture we can see the moving observer's inertial frame, as experienced from HIS point of view, and, much more clearly can we now see the light's relative speed anomaly.



This relative-to-observer acceleration/deceleration of light seems contradictory to evidences gathered by the Michelson-Morley device, which implies that light from two simultaneous events will always reach the observer at the same time (since light cannot accelerate or slow down relative to such observers), independently of the observer's motion (and, by extension, of the observer's inertial frame). Yet Relativity seem to demonstrate how relative speed of light varies accordingly to the observer's motion, so to allow relativity of simultaneity to occur.


At Time's End,

Swan

First Rule of Relativity: The speed of light remains unchanged (if in vaccum, that is), for everyone watching. Vc == vc, always, anywhere. *edit: this is Einsteins second postulate of special relativity, too*

Therefore, the other parameters have to change - lenght and time, as percieved by the people/systems involved or seen from the outside.

Most likely indicated in this case by shifting the signals wavelength to the bluer part of the spectrum.

reply to post by swanne

This is a variant of the Relativity Paradox in another thread, which in the linked post I provided a space-time diagram and link to source explaining why simultaneous events in one frame are not simultaneous in another frame.

You didn't define the problem very well (no specifics thus you can't make calculations), but it looks like you neglected to account for the different clock rates. The speed of light is always the same, according to the clock you use to measure it, but since the clocks are ticking at different speeds, this does create some effects which are not intuitive and thus seem like paradoxes to our intuition. However the paradoxes do not persist with a full understanding of relativity, which very few people have.

Light visible to the observer on the platform will appear 'normal'.

Light visible to the passenger will be expanded if coming from the rear, or 'red shifted', and compressed if coming from the front of the train, therefore 'blue shifted'.

No paradox at all.

It's fixed to our relative time.

reply to post by abecedarian


Yours seems the best explanation. The reason is simple - the wave behaviour of light.

Same is true for sound also.

The wavelenth gets compressed when moving closer and expanded when moving farther.

This is not about time or speed of wave. It is just a spatial effect.

GargIndia
This is not about time or speed of wave. It is just a spatial effect.

I don't think space and time are separate in this relativistic thought experiment. This is why spacetime diagrams are used to solve relativity of simultaneity problems. Here is how the thought experiment is described in wiki and time is definitely mentioned prominently in the explanation (and by the way you can't discuss simultaneity without discussing time):

Einstein's train thought experiment

Einstein's version of the experiment[3] presumed slightly different conditions, where a train moving past the standing observer is struck by two bolts of lightning simultaneously, but at different positions along the axis of train movement (back and front of the traincar). In the inertial frame of the standing observer, there are three events which are spatially dislocated, but simultaneous: event of the standing observer facing the moving observer (i.e., the center of the train), event of lightning striking the front of the traincar, and the event of lightning striking the back of the car.

Since the events are placed along the axis of train movement, their time coordinates become projected to different time coordinates in the moving train's inertial frame. Events which occurred at space coordinates in the direction of train movement (in the stationary frame), happen earlier than events at coordinates opposite to the direction of train movement. In the moving train's inertial frame, this means that lightning will strike the front of the traincar before two observers align (face each other).

The time axis of the spacetime diagram shifts between observers as shown here:

Arbitrageur
The speed of light is always the same, according to the clock you use to measure it, but since the clocks are ticking at different speeds

...relative to each other. But no change is noticed inside each frames. Thus light speed should still be calculated as anomalous.

reply to post by swanne


Why don't you try putting some numbers to the problem? Assume a speed for the train, some distances, and show your calculation for the difference in the speed of light.

Once I see your math, I can see where you're going off the rails, sorry for the bad train pun.

Edit to add: someone posted some math formulas here:

answers.yahoo.com...

Scroll down to post by "oldprof". Didn't check thoroughly yet, but at first glance looks about right. Gives a decent explanation too.

reply to post by Arbitrageur


Good idea, I'll get to it as soon as I'm off work.

Thanks,

Swan

Well, I'm a un-scientist so I'll say my point in layman speak. I think that light speed IS relative but on a scale so small that we don't realize it. Certain environmental factors in Space will slow it down naturally; gravity wells, etc. I mean Gravity bends light, the atmosphere disperses it, and I've even heard that the universe curves it at some point. My point is that light is a physical substance which means that it must obey physical laws. so it must weaken, slow-down, disperse, or whatever it does.

Light speed is relative for sure. It's supposed to be constant in a vacuum but I'm not sure that's correct either because I believe a vaccuum can be cooled but I'm not positive that's the case.
At any rate what I'm getting at is scientist have came really close to achieving absolute ZERO, at the temperature they HAVE achieved they observed the Light/Photon slowed to a fraction of its original speed and were able to observe it.
I read about this a while back, I'm on my phone or I'd link it but I'm sure anyone interested can google it.
So since they can slow light down in controlled environments that means it relative right? At least that's my understanding

reply to post by Arbitrageur


Hang on, I'll be back tomorrow with a more complete reply. I really want to take the time to make a clear reply.

Respects,

Swan

reply to post by swanne

Take your time. It took me years to figure out what I have so if you want to understand it, it's worth spending some time on, and solving a math problem like this is one way to work through some details.

NewsWorthy
At any rate what I'm getting at is scientist have came really close to achieving absolute ZERO, at the temperature they HAVE achieved they observed the Light/Photon slowed to a fraction of its original speed and were able to observe it.
I read about this a while back, I'm on my phone or I'd link it but I'm sure anyone interested can google it.
So since they can slow light down in controlled environments that means it relative right? At least that's my understanding

Not really related to what the OP is talking about, which is a relativity of simultaneity issue.

You probably read some misleading headlines and were confused by them, because I read some whacky sounding headlines about changing the speed of light, but when you get past the BS you find out that no, they never changed the speed of light in a vacuum. There is always some gimmick going on where they say they changed the speed of light, but it's just simply a result of it going through something other than a vacuum.

The Cosmic microwave background (CMB) has a thermal black body spectrum at a temperature of 2.725 degrees above absolute zero; that's about as cold as it gets at this age of the universe, and if you have something that says light doesn't travel at the speed of light in a vacuum at that temperature, saying "google it" doesn't cut it, you'll have to post a source.

Of course light does not appear to travel as quickly through anything other than a vacuum (like glass, water, etc, and you can play all kinds of games with those effects as some may be temperature dependent). But that is more about the way photons interact with different materials, and has little to do with the speed of light in a vacuum changing which is always a constant according to relativity.

reply to post by Arbitrageur


I understand you are coming from. Einstein has such an effect on people that "time" has become variable in every possible situation.

But Einstein is wrong here.

Time does not contract and expand, it is "space" or distance. Many observations are based on our perception of space. This is what we see everyday, every second.

reply to post by GargIndia

Yes there are spatial effects, but there are also well established time effects, and this isn't "where I'm coming from", it's what many peer reviewed scientific experiments testing relativity have shown.

Lots of people are trying to prove Einstein's theory incomplete, and it probably is some way as Newton's classical mechanics was incomplete but still matched experiment very well for centuries. Relativity can't deal with quantum mechanics, which is why we need a theory of quantum gravity, so nobody is claiming Relativity is the answer to everything.

However, the time effects of relativity have been proven not only in many different experiments, but in the GPS system too, so given that nearly all experiments where relativity applies have confirmed time dilation effects, undergoing peer review etc, it's hard to see how a person posting "Einstein was wrong about relativity" about time dilation, with no evidence to support that claim, can expect the claim to be taken seriously.

reply to post by Arbitrageur


All right, let's see.

Before I start, please remember that in this thread, I am NOT attempting to falsify Einstein's Relativity of simultaneity. I am simply discussing the fact that Relativity of Simultaneity naturally implies Relativity of Speed of Light, which is not a bad thing but nevertheless still is in contradiction with our current understanding of light.

Okay. My maths are VERY rusty, but I'll give it a try:

Let us imagine that the train is 4 x 299,792,458 meters long.

The observer is in the center of the moving train. There is 2 x 299,792,458 meters between him and each ends of the train.

Let us also imagine that the train moves at the speed of 1/2 c.

As the train rushes at 1/2 c, the two lightning bolts simultaneously strike both ends of the train, generating Event A (on the rear) and Event B (on the front).

Because of the train's velocity, it doesn't take 2 seconds for the light from Event B to reach the observer, but in fact 1.3 second (d/(c+v) = 2/(1+0.5) = 1.3). This creates the illusion that Event B happened before Event A.

Because of the train's velocity, it doesn't take 2 seconds for the light from Event A to reach the observer, but in fact 4 seconds (d/(c+v) = 2/(1+-0.5) = 4). This creates the illusion that Event A happened after Event B.

This shows that for Relativity of Simultaneity to occur, Relativity of Speed of Light must exist.

Since this seems in contradiction with current understanding of light, one may invoke length contraction and/or time dilation as a solution. But again, this only resolves one Event out of two, never both:

If length contraction occurs at relativistic speed, to the point of transforming 3 x 299,792,458 meters into 2 x 299,792,458 meters, then this may indeed solve the Event B's anomalous light speed:

3/(1+0.5) = 2 seconds for 2 x 299,792,458 meters (as perceived by the observer inside the train) = normal speed of light

But such contraction does not solve the Event A light speed anomaly:

3/(1+-0.5) = 6 seconds for 2 x 299,792,458 meters (as perceived by the observer inside the train) = abnormal speed of light

In fact, such length contraction renders the Event A speed anomaly even more at odds with the Michelson-Morley experiment.


If time dilation occurs at relativistic speed, to the point of slowing 1.3 seconds to 2 seconds (transformation ratio: 0.65), then this may indeed solve the Event B's anomalous light speed:

(2/(1+0.5))/0.65 = 2 seconds for 299,792,458 meters (as perceived by the observer inside the train) = normal speed of light

But such dilation does not solve the Event A ligth speed anomaly:

(2/(1+-0.5))/0.65 = 6.153 seconds for 299,792,458 meters (as perceived by the observer inside the train) = abnormal speed of light

In fact, such time dilation renders the Event A speed anomaly even more at odds with the Michelson-Morley experiment.


So... there is it. Something keeps on showing up, and that's the apparent relativity of the speed of light.

Is it possible that the Michelson-Morley device was not capable if detecting evidences of relative speed of light for an observer moving below 0.0001 c?





Regards,

Swan

swanne
Before I start, please remember that in this thread, I am NOT attempting to falsify Einstein's Relativity of simultaneity. I am simply discussing the fact that Relativity of Simultaneity naturally implies Relativity of Speed of Light, which is not a bad thing but nevertheless still is in contradiction with our current understanding of light.

I think what you mean is you see a contradiction with your understanding. "Our understanding" often refers to mainstream science views and there's no contradiction in understanding of this topic in mainstream science that I'm aware of.

Since this seems in contradiction with current understanding of light, one may invoke length contraction and/or time dilation as a solution. But again, this only resolves one Event out of two, never both:

As I already explained, both time and length are affected (see the Minkowski diagram I posted above), so you have to make adjustments to both, and you didn't do this anywhere that I can see.

Arbitrageur
As I already explained, both time and length are affected (see the Minkowski diagram I posted above)

But... to work, this diagram supposes a preferred frame of reference. Otherwise, how can the guy in the train be sure that HE is the one moving in the first place?

, so you have to make adjustments to both, and you didn't do this anywhere that I can see.

I could do that later when I'll be off-work, but the result will be the same: it'll resolve only one out of the two Events. That's because length dilation is needed to resolve Event A's anomalous speed of light.

reply to post by swanne

In your example the events happen simultaneously in the fixed observer frame of reference. For the observer in the moving train, they won't happen at the same time (apply lorentz transformation to get the numbers). -> Relativity of Simultaneity