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

moebius
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

My point exactly. But this implies Relativity of Speed of Light, which is not always recovered by length contraction and time dilation.

That's because for non-simultaneity to occur, one light ray (the one from Event A) must reach the observer at a slower relative speed than the other ("the other" being the light from Event B). Otherwise both events would be observed as simultaneous again.

swanne

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?

Here is the diagram again.

Einstein's train thought experiment


It shows one reference frame on the left, and the other reference frame on the right. In relativity, it's not proper to say one is preferred. Both frames of reference are equally valid, so it doesn't matter which one you use. You can start with either observer, and use relativity math to figure out what the other observer would observe given the same events.

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.

It's no illusion. Either perspective is equally real. We humans have some difficulty wrapping our mind around this concept which I guess is why it took centuries for relativity to be discovered. It's not so intuitive.

swanne
That's because for non-simultaneity to occur, one light ray (the one from Event A) must reach the observer at a slower relative speed than the other ("the other" being the light from Event B). Otherwise both events would be observed as simultaneous again.

One thing I noticed in your math, is not so much a math issue is a lack of clarity on which reference frame you are doing the calculations in. You pick one frame or the other, and the speed of light is the same in each. It's the clock rate (time) and length (distance) that's different in the different frames, not the speed of light. If you come up with a different speed of light in the two different frames, you did the math wrong.

Eimdsteimn's Train Thought Experiment

When we take the ratios dS/dT = ds/dt = c, we see the only way c can be the same for the outside observer (dS/dT) and the passenger on the train (ds/dt) is for both space and time to adjust to make it so. And that's what happens.

reply to post by Arbitrageur


Oh, ok now I see what you're saying. I considered your diagram



And I drew the path of the two light rays.



I realize now that in the non-moving frame, light rays each crosses 5 squares before reaching the stationary observer. In the moving frame, light rays each crosses 4 warped squares before reaching the moving observer. Thus these rays are technically going at the same speed relative to one another, even though the observer will still view them as separate events.

Okay, so Light does travel at constant speed, no matter what frame, after all (for this to work, though, it seems length behind the moving observer gets dilated, right? ).

I apologize since it took me all that time to get it. You did provide the diagram in Page 1... I didn't realize what you meant... My mistake. Sorry.

My sincere Thanks for your patience.



Swan

reply to post by Arbitrageur


One last question, unrelated to the OP topic.

Since no frame can be taken as a preferred reference frame, then why does the Events (lightning bolts) position in both frames stays locked to the Stationary frame, as such:



If no preferred frames can exist, then the Events (well, that is, their space-time coordinates) cannot "prefer" one frame's system over another... and should tilt like the rest of space-time in a moving Minkowski spacetime...

swanne
Okay, so Light does travel at constant speed, no matter what frame, after all (for this to work, though, it seems length behind the moving observer gets dilated, right? ).

See this link and scroll down to the section on "The Relativity of Time, Mass, and Length", and read the section about length, which hopefully explains how the length is perceived


The Relativity of Time, Mass, and Length

I apologize since it took me all that time to get it. You did provide the diagram in Page 1... I didn't realize what you meant... My mistake. Sorry.

My sincere Thanks for your patience.

You're welcome and I'm glad you're on the path to figuring this out. If it was easy, it wouldn't have taken centuries after Newton for someone to figure out. It's not easy or intuitive.

swanne
One last question, unrelated to the OP topic.

Since no frame can be taken as a preferred reference frame, then why does the Events (lightning bolts) position in both frames stays locked to the Stationary frame, as such:

That's actually a good question. The lightning bolts do not stay locked to the stationary frame. The lightning bolts are specific events in spacetime, and as such their positions do not change in a spacetime diagram when the frame of reference is changed. That's why we use spacetime diagrams.

Now when you draw the Minkowski spacetime diagrams which consider two reference frames, normally you pick one that has right angles of time versus distance, then the other reference frame will NOT have right angles between them. The selection of which one has right angles is arbitrary.

You can redraw the spacetime diagrams with frame A having right angles and frame B having non-right angles as was done here, or redraw them so that frame B has right angles, in which case frame A will not have right angles. But whichever arbitrary reference frame you choose, if you've drawn the space time diagram correctly, space time events will not move once you have picked whichever one you want to have right angles and draw the other one with non-right angles. In fact, here is a good illustration showing how three reference frames can be shown on the same spacetime diagram. You see events A B and C simultaneously from one reference frame (say an observer on the ground), then the other two frames could represent trains traveling in opposite directions, one at +0.3c and the other at -0.5c:

Relativity of simultaneity

Events A, B, and C occur in different order depending on the motion of the observer. The white line represents a plane of simultaneity being moved from the past to the future.

That's from the link in the first post in this thread I made, but I don't know if you saw it so I figured I'd repost it since if you can figure out what's going on in that animation it should answer your question.

As another example, see this spacetime diagram where it's redrawn with right angles for each reference frame, which is mathematically equivalent and either way is equally valid (scroll down to the spacetime diagrams section):

english.turkcebilgi.com...

Similarly, you could redraw the gif animation above for the other two frames and all three will look different, but they will all be mathematically equivalent. The reference frame that's shown with right angles is arbitrary. The other two versions you could draw would give right angles to the other two reference frames. The representation of the sequence of events would be similar no matter which frame you choose to draw with the right angles.

Space and time are inextricably linked. That’s why it’s called spacetime. Time dilation occurs whenever you move through space. As you drive down the road your clock literally tics more slowly as viewed from the reference frame of a stationary observer. It’s an established fact, proven experimentally over and over again. The gps satellites have to take this into account in order to provide accurate information.

These effects aren’t intuitive and are difficult to get handle on. In our day to day lives we don’t perceive relativistic effects. The mathematics, however, are logically consistent and tight as a drum.

reply to post by netbound


My dear friend, you forget that we take measurements of all parameters. The field of measurement is called 'metrology'.

We measure time using some method. We have built clocks for that purpose. There are several types of clocks, each type using a specific method.

When you say 'time dilation' occurs on a moving object wrt to a stationary object, the difference is being shown/computed as difference between two clocks present in these two objects.

We have assumed an atomic clock to be precise whether in a 'Stationary' or 'moving' object? This is an assumption that needs revisiting.

When you place a clock on a satellite, the distance between that satellite and earth is essentially fixed. There is no movement of satellite relative to earth (it is not coming closer or going farther from earth). So relativistic effect should not apply. Why clock on a satellite is showing different time from the one on earth? Please answer this question.

GargIndia
When you place a clock on a satellite, the distance between that satellite and earth is essentially fixed. There is no movement of satellite relative to earth (it is not coming closer or going farther from earth). So relativistic effect should not apply. Why clock on a satellite is showing different time from the one on earth? Please answer this question.

It's not the distance from Earth that's changing, it's the position. If a clock is on the ground in London, and the satellite clock travels overhead from New York to Moscow, there is relative motion.

But that effect which makes the GPS satellite clock run slower is small compared to the other, larger effect which makes the clock on the ground run slower (gravity), so that's why we see the satellite clock run faster instead of run slower which is what the relative motion makes it do. The two effects only partially cancel each other out but with GPS satellites the gravity effect wins.

In lower orbits like the ISS the gravity effect doesn't win and the clock on the ISS does run slower, so whether the clock in orbit runs faster or slower depends on the orbit altitude as seen in this graph:

Time dilation due to gravitation and motion together

Daily time dilation (gain or loss if negative) in microseconds as a function of (circular) orbit radius r = rs/re, where rs is satellite orbit radius and re is the equatorial Earth radius. At r ≈ 1.497 [Note 1] there is no time dilation. Here the effects of motion and reduced gravity cancel. IIS astronauts fly below, whereas GPS and Geostationary satellites fly above.

So there is a single altitude where clocks in orbit run at the same speed as ground clocks, but most orbits are above or below this altitude.

reply to post by Arbitrageur

Thanks Arbitrageur for your reply to GargIndia. You stated it a lot more intelligently than I would have. I probably shouldn’t have used gps as an example - It seemed to confuse the issue, since most folks seem to think that gps satellites are in geostationary orbits.

reply to post by netbound

You're welcome, and thanks for explaining GargIndia's question. I didn't understand that they were thinking the GPS was geostationary (and you're right that it's not), but that's a good guess which makes the question make more sense.

Given that perspective, I actually have a little clarification about Geostationary satellites for GargIndia. Get a string 2 meters long and affix a ball at one end and affix another ball in the middle of the string.

Grab the end with no balls and whirl the string overhead. With every rotation, the ball on the end covers a circumference of 2*pi*2m and the ball in the middle of the string covers a circumference of 2*pi*1m, so the outermost ball is covering a lot more length with each rotation, and it must travel faster to do so.

Now imagine the outermost ball represents a geostationary satellite, and the ball in the middle represents the Earth's surface, you have a model of a geostationary satellite, sort of. The inner ball looks "up" (actually you'd call it "out)" and always sees the outer ball directly "above" (outward of) it, and the distance between them doesn't change, but since the outer ball is moving faster, it has time dilation relative to the inner ball just as the geostationary satellite has time dilation relative to a fixed position on the ground it stays above. So even geostationary satellites have time dilation due to motion, but the effect of reduced gravity is much more influential as the graph shows (see GeoStat on the graph).

GargIndia
reply to post by netbound

 

My dear friend, you forget that we take measurements of all parameters. The field of measurement is called 'metrology'.

We measure time using some method. We have built clocks for that purpose. There are several types of clocks, each type using a specific method.

When you say 'time dilation' occurs on a moving object wrt to a stationary object, the difference is being shown/computed as difference between two clocks present in these two objects.

We have assumed an atomic clock to be precise whether in a 'Stationary' or 'moving' object? This is an assumption that needs revisiting.

When you place a clock on a satellite, the distance between that satellite and earth is essentially fixed. There is no movement of satellite relative to earth (it is not coming closer or going farther from earth). So relativistic effect should not apply. Why clock on a satellite is showing different time from the one on earth? Please answer this question.

Why clock on a satellite is showing different time from the one on earth?

light speed is not constant ! it is related to gravity.

... I see Arbitrageur already explained that

KrzYma
light speed is not constant ! it is related to gravity.

... I see Arbitrageur already explained that

I said clock speed is related to gravity.

Light speed is constant, and does not vary, even in varying gravitational fields (according to theory and observations).

The frequency (or wavelength) of light does vary due to gravitational fields however, which we call "red-shift" or "blue-shift".

Arbitrageur

KrzYma
light speed is not constant ! it is related to gravity.

... I see Arbitrageur already explained that

I said clock speed is related to gravity.

Light speed is constant, and does not vary, even in varying gravitational fields (according to theory and observations).

The frequency (or wavelength) of light does vary due to gravitational fields however, which we call "red-shift" or "blue-shift".

sure, gravity shifts the whole EM spectrum a bit, which also means the whole interaction in EM field shifts a bit, that's why something like time dilatation happen to be observed.

I'd say it's relative. Even Einstein himself thought this for a while until an that experiment measuring gravitational light deflection around the sun during an eclipse. He couldn't get the math right until pushing one relativity theory aside for another one. (So Einstein may have thrown out the baby with the bathwater. However some later revisions by others researching the topic seem to be able to make it work again while using general relativity.) It's kind of an interesting thing to read about.

Hate citing Wikipedia too much, but this is a good one:
Wikipedia article on Variable Speed of Light

Anyhow speed is a ratio of distance over time, and for light to bend gravitationally it has to speed up or slow down. Fresnel explains this quite well with light passing through a medium, but in a vacuum spacetime itself is the medium. The thing is that the ratio that defines that speed is also altered such that you were at a location relative to where that speed is different or changing, you'd still see it as a constant. So although it appears constant, think of c as a coefficient of distance (space) relative to time. (Some coefficients remain fixed to appear as a constant, but the variables that define them are not.)

So if you were on that train approaching lightspeed, time or space would be expanded or compressed such that d/t still equals the known value of c for that frame of reference. So that light approaching the window of that train speeds up or slows down in accordance with "space-time density". It's also likely that this ratio can be expressed in gravitational flux or a change in energy density which is often equated to mass. (But I think you don't really get heavier, time instead slows down on your end. However the equivalent of that mass could be expressed in terms of inertia you'd be carrying if you were to hit something.)

Some people don't like this however because there's no frame of reference for time. But I'd say to go with it. It raises some oddities, but I'm willing to accept that parts of the universe that are affected by massive objects age different than those which are not. So our star system could be much older than than those near the center of the galaxy, and some other things that would confound prevailing theories like red-shift and universal expansion. No real way to determine the overall age of the universe either, but you could find an average. It's also something which may raise loopholes that offers great opportunities if you can apply engineering to what the math and physics says.

reply to post by pauljs75


"Light bending around the sun"

Are you sure it is due to 'gravity'.

The stars and interstellar clouds represent regions of high energy in space. It is possible that light is affected by these regions.

'Space' is an item which is least explored and understood by humans. So no need to hurry up until all variables are in place.

GargIndia
reply to post by pauljs75

 

"Light bending around the sun"

Are you sure it is due to 'gravity'.

The stars and interstellar clouds represent regions of high energy in space. It is possible that light is affected by these regions.

Energy bends light too but unless you can find an example to the contrary (and I doubt you can), it's negligible. I'll show you how to do the math for the sun.

The mass of the sun is 1.981E30 kg, which is what determines its gravitational influence.

The energy from the sun is created by converting about 4.29E9 kg per second into energy.

Now you know it takes about 8 minutes for sunlight to reach Earth, and when astronomers look at stars near the sun during an eclipse they are looking at stars relatively close to the sun, meaning the sunlight has only traveled a few seconds before it reaches the apparent position of the star they are looking at. So let's call that period of time 10 seconds, though you can vary it as needed for a specific stellar observation during an eclipse if you wish. That math is simple; just multiply the energy per second by 10 seconds so the energy within 10 light seconds of the sun's photosphere has an equivalent mass of 4.29E10 kg.

Now how much effect does this have? Divide this energy by the sun's mass and you get:

4.29E10 kg/1.981E30 kg = 2.16E-20 which is an effect of 0.0000000000000000000216 or 0.00000000000000000216%

So, this is the magnitude of the energy effect and there are probably much larger measurement errors so in any practical calculation I assume that term is considered negligible. That makes sense really if you consider that the sun's life is estimated at 10 billion years and the energy emitted by the sun in 10 seconds is only 10 seconds out of 10 billion years, and that overestimates the fraction because the sun will still have a lot of mass left at the end of its life.

Now the reason I suspect you can't find an example of concentrated energy is that energy tends to dissipate (as it's radiating in all directions from the sun for example) in contrast to mass which tends to aggregate due to gravity. There might be a case where the energy component is not negligible, maybe with a pulsar, but I suspect even then it's pretty small effect.

Here is a similar answer from a university:

Q & A: Can you bend light with light?

Yes, in principle but not in any practical sense. The fact that mass can bend light is a well calculated and well measured phenomenon. The first example occurred soon after Einstein developed the general theory of relativity. The measured deviation of distant light from stars was measured during a total eclipse of the sun. The bending angle is proportional to mass of the object causing it. The mass of the sun is enormous but the measured angular deviation was only about 1.5 arc seconds, 0.0004 degree.

The effective mass of any light source that I can think of would not even come close to a microgram of equivalent mass energy. No way can you measure the corresponding deflection it would cause a light beam. Still it's an interesting question, just don't hold your breath.

I didn't limit the calculation above to just light. By using the mass conversion rate, it should account for all the energy produced by the sun (excepting blips like solar flares/CMEs, or other temporary variations from the norm) even forms of energy beyond the visible spectrum of light.

'Space' is an item which is least explored and understood by humans. So no need to hurry up until all variables are in place.

We certainly have a lot to learn about space (like the nature of dark energy or vacuum energy), but the bigger mystery regarding light getting bent is, what is the source of "dark matter" which seems to bend light more than the visible objects can account for. Until we solve that mystery, our understanding about what exactly is bending the light is incomplete.

reply to post by Arbitrageur

The lightning bolts are specific events in spacetime, and as such their positions do not change in a spacetime diagram when the frame of reference is changed.

Makes sense. Events are points which crosses all frames, and their unchanging nature is a requirement for Relativity to work. It's only our space-time coordinate system which we use to measure these events that changes with each frames.

Now when you draw the Minkowski spacetime diagrams which consider two reference frames, normally you pick one that has right angles of time versus distance, then the other reference frame will NOT have right angles between them. The selection of which one has right angles is arbitrary.

Indeed; nicely put.

In fact, here is a good illustration showing how three reference frames can be shown on the same spacetime diagram. You see events A B and C simultaneously from one reference frame (say an observer on the ground), then the other two frames could represent trains traveling in opposite directions, one at +0.3c and the other at -0.5c:

Relativity of simultaneity

Events A, B, and C occur in different order depending on the motion of the observer. The white line represents a plane of simultaneity being moved from the past to the future.

That's from the link in the first post in this thread I made, but I don't know if you saw it so I figured I'd repost it since if you can figure out what's going on in that animation it should answer your question.

Nice animation, thanks for posting it! It's quite a good reminder of how the phenomena works, I'll be saving it onto my computer.

Similarly, you could redraw the gif animation above for the other two frames and all three will look different, but they will all be mathematically equivalent. The reference frame that's shown with right angles is arbitrary.

Good point, I'll keep that in mind.

It's not easy or intuitive.

Hehe, wait until you pick up a guitar... lol

Seriously though: Einstein was a genius. I'm glad you gave me the opportunity to understand his work better. It's just a bit... disappointing that after one century, so few of us people really know what he meant.

reply to post by Arbitrageur


First of all, I appreciate you by replying in a very sensible and thoughtful manner.

When I said 'regions of high/intense energy in space', I was not exactly referring to light.

There are many manifestations of energy, and one is "electro-magnetism". Electro-magnetic forces are very strong compared to gravity.

As far as the effect of gravity on waves, you can run experiments using sound waves in lab. You can simulate higher gravity in lab, and you can measure the properties of sound in the medium present inside your apparatus.

It seems further in the thread you solved your problem in the OP but to me its quite simple, the relativity aspect is with the observer (if one observer is moving towards an event(incoming light wave)compared to an observer staying stationary, the observe moving toward will experience the event sooner(simple analogy would be in a still water swimming pool one person in the middle, two people drop bowling balls at the sides, on person is on a surfboard paddling towards one of the sides, they will experience the waves at different times, though they were simultaneously created). The fact that charged matter is coupled to a/the 'EM field' means that all calculations can start at the moment EM radiation is created, I think in that regards it is used as the posts to measure aspects of reality. But its still quite sketchy, being as there isnt much clue as to what the EM field is or how it exists, if it moves, or how it is even coupled to charged matter. But in the realm of matter, and with desire of measuring contextual relationships of material, it seems no matter how charged matter is spinning and densely clustered and revolving and traveling, if it is accelerated at that moment, some relation involving the difference of the energy used to accelerate will 'immediately' cause a disturbance in the em field, and I suppose its just one of those things that has to be expected, whatever the EM field is, whatever charged matter is, when it is accelerated, the EM field how ever it is connected, reacts at the speed of light.

Now about things being able to go faster then light, we must admit that regardless of anything regardless there is a finite amount of energy that exists, obviously, so in any manifestation of a reality there must be some speed limit, if all the energy in the universe was (yes very) hypothetically stored into a dense state to use as a propulsion of some kind to see how fast an atom could be accelerated through...vacuum?nothing? Perhaps that would result in it going faster then the speed of light, but who would know at that point, and who knows how we would be able to measure and compare, what light speed would even be in that circumstance so yea, idk anything.

reply to post by ImaFungi


You have given a very good example.

However take the example of a ship and human occupants of that ship.

Let us assume the ship is moving at the speed of light.

Now for the occupants, everything in the ship is moving at same speed as them, so there is zero relative velocity. So the occupants should see everything just as normal.

Assume there are some lights on on the console. The operator of the console should see the light just as normally as a stationary ship, as the eyes of the operator are moving towards the source of the light just as fast as the source of the light is moving away.

So "relativity" is not an important concept at all. It is only causing confusion in science.

Everything is moving in space. The earth is moving, along with its occupants. The sun is moving along with all its planets. The galaxy is moving along with all its suns. Still we are able to perform all our stuff normally.