# Scenario in an attempt to understand relativity

1. Mar 19, 2011

### CosmicVoyager

Greetings,

I am trying to figure out how that can be that everyone can measure all light from any source to be the same speed no matter the speed of the measurer or the source. It seems that the photons would have to be in different places depending on where the person doing the measuring is and at what speed they are traveling.

What would happen in this scenario:

If a year after a photon is emitted, there is an object, which is stationary relative to the source, a light year away in the path of the photon, then the photon will be there and be absorbed. And the light will seem to have taken one year to travel one light year. Correct?

Now, if instead, a year after the photon is emitted (according to clocks at the source and first object), there is an object which is moving (relative to the source and first object) and therfore experiencing time dilation (relative to the source and first object), in the same place as the first object, will the photon be there and be absorbed? Since clocks would be running slower for that object, it would measure the light to have taken less time to travel the light year. So it seems that it would *not* detect the photon. It seems that the second object would have to be in a different location to detect the same photon that the first object would. It seems that whether the photon is at a location depends on the relative speed of an object that would be there to detect it.

Thanks

2. Mar 19, 2011

### bcrowell

Staff Emeritus
The distance covered by the photon is Lorentz-contracted in the frame of this object.

3. Mar 19, 2011

### ghwellsjr

When we talk about everyone measuring the speed of the same light burst (I'd rather talk about a bunch of photons because, as you pointed out, if you're talking about a single photon, as soon as it gets absorbed by one observer, it ceases to exist and cannot therefore be observered by anyone else), we are always talking about a round trip (another thing a single photon cannot do) involving reflection from a mirror a measured distance away. Each observer will have their own mirror and so there are two different reflections. The time it takes to go from an observer to his mirror and back to the observer is what is used for that observer to calculate the round trip speed of light. A second observer moving with respect to the first will do the same thing with a different portion of the light and because his ruler is contracted and his clock is running slower will calculate the same speed for the round trip of the light.

4. Mar 19, 2011

### CosmicVoyager

Isn't Lorentz contraction parallel to the direction of movement?

I mean for the second object to be moving perpendicular to the path of the photon from the source, and to cross the path at the location of the first object when the first object's clock would indicate one year had elapsed. So the second object would be at the same location as the first at the same time (according to the first's clock) and without Lorentz-contraction in the direction of the photon source.

5. Mar 19, 2011

### bcrowell

Staff Emeritus
OK, in that case have you tried writing out the Lorentz transformation in 3+1 dimensions and checking that it comes out consistent? The Lorentz transformation is essentially designed so that it will give consistency for the speed of light.

6. Mar 19, 2011

### CosmicVoyager

I don't know how. lol If the second object would still detect the same photon, could someone explain in english how that can be :-) For example, if the second object were moving parallel, the reason would be that length is contracted between the object an the source. What is the reason if it is moving perpendicular?

7. Mar 20, 2011

### ghwellsjr

You're conflating many different concepts here which makes it very difficult to address your concerns. I think what you want to know is how time dilation and length contraction work to cause a moving observer to get the same answer for the speed of light when the light is traveling either perpendicular or parallel to his direction of motion since there's no length contraction in the first case but there is length contraction in the latter case. Is that correct? But I'm not sure you understand either of these two cases, is that correct?

You're also talking about the light starting at one source where there is no observer, and traveling for one light year before it arrives in the vicinity of an observer who is stationary to the light source and another observer who is moving with respect to the light source. And you want to use the time that it takes for the entire trip in your measurement. And you want to use a single photon. And you want the second moving observer to travel perpendicular to the path of the photon. All this makes for a very difficult, if not impossible scenario to discuss. I'm not even sure how to configure what you have in mind.

I already mentioned the problems of using a single photon:
1) A single photon cannot be observed by two different observers.
2) A single photon can only go in one direction.

I already mentioned the fact that a measurement of the speed of light must involve a round trip and the observer has to be located at the start of the trip and at the end of the trip. So your idea of light starting a light-year away where there is no observer and using that distance and the time it takes for light to travel that distance is not a measurement. To make a measurement of speed, you have to have a ruler and a stop watch and you calculate the speed by dividing the total distance by the total time. These are ideas the Einstein discussed in his 1905 paper where he introduced Special Relativity to the world. We would be wise to follow his example.

So can we please change your scenario into something more conventional? I suggest that you consider a very popular Special Relativity issue, which is sometimes called a paradox. It goes like this:

We have two observers, I, George, will be the first one and we'll assume that I'm stationary and I have a flash bulb that I have arranged to be energized when you, the CosmicVoyager traveling toward me in a straight line at half the speed of light arrive at my location. You carry a stop watch, as do I, which we both start at the moment of the flash. You continue on without stopping or slowing down. The very bright flash of light will expand outward from its starting point in a perfect sphere getting bigger at the speed of light. According to Special Relativity, I will measure myself to be in the exact center of the expanding sphere of light. That makes sense, doesn't it, since I set off the light and I'm not moving? But according to Special Relativity, you will also measure yourself to be in the exact center of the expanding sphere of light and that doesn't seem right, does it, because you are moving with respect to the source of the light? But would it make sense if you were the one carrying the light source and to have set it off when you arrived at my location? Maybe, but in this case, I, too, would measure myself to be in the center just like you would. And that doesn't seem right but it really doesn't matter what the speed of the source of the light is or the speed of the observers, they all will think they are in the center of the expanding sphere of light. This can only work if the speed of light is the same for all observers, do you agree with that?

So how do we observe or measure this expanding sphere of light? Well, once it has traveled away from us, we can have no awareness of its existence or its progression through space unless we place some detectors out in space to tell us when the light arrives at a given location. We could, in principle, wire up some light detectors with long wires to let us know when the light hits them but this has the disadvantage that we would have to take into account the propagation of the signal along the wire back to us. A better idea, in fact, the best idea is to place a bunch of mirrors out in space, all a constant distance away that will simply reflect the light back to us and then if we see the light arriving from all mirrors simultaneously we will know that we are in the center of the expanding sphere of light and we will stop our stopwatch when that happens and calculate the speed of light by taking twice the distance and dividing by the time.

Now it's important to realize that we each must have our own set of mirrors because you are traveling with respect to me and your mirrors must be traveling at the same speed as you are. So I take my ruler and carefully place them some constant distance from me and aimed back toward me. My mirrors will form a perfect sphere. You do the same thing with your ruler except that since you are moving, your ruler is length contracted whenever it is parallel to the direction of your motion. But your ruler is the same length as mine when it is perpendicular to your direction of motion and somewhere in between for other angles. So your mirrors will not form a perfect sphere like mine will but rather a somewhat flattened sphere. However, to you it looks like a perfect sphere because you, too, are flattened in the same way.

Now what happens when we carry out out test? Well it's a little difficult to describe in words so I have created a little animation that depicts what happens:

In this video, I, the stationary observer, am depicted in green and you, the moving observer, are depicted in red. Our mirrors are in yellow. The outgoing expanding sphere of light is depicted in blue and the collapsing sphere of light reflecting off my mirrors is shown in green while the collapsing sphere of light reflecting off your mirrors is shown in red. Now you will note the shape of my mirrors form a section through a perfect sphere whereas the shape of your mirrors is compressed along the direction of your motion.

Now if you follow the progression of the light as it is expanding, it forms a perfect circle and hits all my mirrors at the same time which forms a perfect shrinking circle that collapses on me from all directions simultaneously, taking a particular amount of time which when divided into the total distance yields the correct measure of the speed of light.

Now what happens with your mirrors? It turns out that the light does not hit all your mirrors at the same time but what does happen is they create a perfect shrinking sphere of light but repositioned to collapse on you at just the right time as required by Special Relativity according to time dilation (a lengthening of time).

It's important to realize that what we see of the progression of light in the animation is not available to us as observers in the animation. We, as observers in the video only know about the beginning of the flash and the separate returns of the reflected flashes off our individual set of mirrors.

Let me know if this helps you with your question or if you have any more questions.

Last edited by a moderator: Sep 25, 2014
8. Mar 20, 2011

### CosmicVoyager

That is awesome! Thanks :-)

I will think about it some more and see if it raises any questions. I took a conceptual basic physics class which focused on understanding. I wish there was a conceptual relativity class, and a conceptual quantum physics class.

We know that time dilation is more than a technique to make things work out. We have actually measured it with pairs of high precision clocks. Is there a way to measure length contraction to know objects are actually getting thinner? Since density is increasing, it's gravity should be affected. You could pass in front or behind it closer to it's center since it is narrower and experience stronger gravity.

Last edited by a moderator: Mar 24, 2011
9. Mar 20, 2011

### ghwellsjr

Measuring time dilation requires that length contraction must also be happening, or else it would be possible to build a clock that would keep different time depending on its orientation with respect to the direction of motion, don't you think?

Also, keep in mind that a clock is accumulating time dilation which is the reason why we can see a difference between the clock that took a trip and the one that remained stationary. Once the two clocks are brought back together, there is no more difference in time dilation for them, as they tick at the same rate. If we took a metronome (which is the ticking portion of the clock without the accumulator) on a trip and left one at home, we would not be able to demonstrate time dilation because whenever we brought them back together for comparison, they would be ticking at the same rate.

If we could devise a similar instrument, like an odometer, that would accumulate length contraction of the distance traveled, then we would see that taking two such instruments on the same path at different speeds would measure different length accumulations. Actually, we can build such instruments but they have no where near the precision, stability and accuracy to demostrate length contraction, but maybe some day we will.

But to me, the fact that traveling clocks demonstrate time dilation without regard to their orientation is proof enough that length contraction is also being demonstrated, otherwise, it would be possible to devise a clock that would be sensitive to its orientation and we could take two or more of them on the same trip and they would keep accumulate different times.

10. Mar 24, 2011

### CosmicVoyager

Okay, I have run into a problem with the idea that objects get narrower the faster they move.

If I were to measure out the distances between my mirrors when I am stationary to you, and I and all of the mirrors were to accelerate together, then they should still be arranged in a circle because as the mirrors narrow, the space between them increases since they are not connected.

This also got me to thinking more about what is happening when an object narrows. Objects are made up of smaller objects, and it is actually the smaller objects that are narrowing, and when when they do, the space between them increases. The length of the larger object would stay the same if it were not for the forces binding solids together, and the object should be torn apart if accelerated quickly enough. The edges of the object would undergo the most strain since they would move a longer distance toward the center. It seems like we should be able to measure this.

11. Mar 24, 2011

### Janus

Staff Emeritus
No. Length contraction is not something that "physically" acts on objects. It means that reference frames in motion with respect to each other measure the length differently. In other words, if there are two points in space that are 1 meter apart according to you, for someone traveling parallel to the line joining them, these two points will be closer together, regardless of the fact that there is no physical connection between those points or even if there is any physical objects at those point.

So in your above examples, the distances between the discreet objects also length contract.

12. Mar 24, 2011

### ghwellsjr

You are correct when you say if the mirrors accelerate together, you mean that you put individual rockets on each mirror and accelerate each of them with no rigid connectors between them but if you mean they are fastened to some kind of structure and you have only one rocket that accelerates the entire structure together, then the mirrors will move closer together.

And you are correct when you talk about an "object should be torn apart if accelerated quickly enough". Yes, yes, yes, but when we discuss these thought problems in relativity, we ignore all these issues that would bring us down to reality because there are so many of them and we can't do anything about them anyway. So we pretend. The only things we can actually accelerate to these speeds are atomic particles and all experiments that can and have been done support the conclusions of special and general relativity.

13. Mar 24, 2011

### CosmicVoyager

"Length contraction is not something that "physically" acts on objects."

Okay, this is what I was afraid of. It seems to me this "length contraction" idea is just a convenient mathematical correction to compensate for something we have no explanation for, made up so that things will work out in calculations so that it can be predicted how things will *appear* in different circumstances. It is not really happening. Rulers are not contracting. And space is certainly not expanding and contracting based on how fast an object is moving. So it is extremely misleading to say objects flatten the faster they go. The correct answer for how it is that the speed of light can be measured to be the same regardless of one's speed is "No one knows. We only know how to calculate what the results of measurements will be."

Last edited: Mar 24, 2011
14. Mar 24, 2011

### Rap

Suppose you have a cube and you shine a light on it, and look at its shadow on a screen. If you orient it right, its shadow will be a square. If you rotate the light and the screen properly, you can make the shadow look like a hexagon. When you say "it is extremely misleading to say objects flatten the faster they go.", that is like saying "it is extremely misleading to say a square turns into a hexagon when you rotate the light and screen".

The square and hexagon are only 2-dimensional shadows of the real thing - the cube. What is the true shape of a cube? Is it square or hexagonal? Neither, its a 3-dimensional object. In the theory of relativity, when you talk about the length of an object, you are talking about a shadow of a 4-dimensional object that exists in space and time. Different inertial frames view this 4 dimensional object in different ways. They measure different lengths of the object, different shadows. When you are at rest with respect to the object, you see a shadow which is longer than any other shadow, its called the "rest length".

Just like when you look at the shadow of a cube, the square shadow is special - no other shadow has a smaller area. But so what? Basically, Einstein realized that its all about the cube, not about its shadows. He developed the geometry and physics of 4-dimensional spacetime, and explained how different inertial frames saw the shadows that resulted. This is more than saying that he just came up with a bunch of equations that worked and had no idea what they meant.

Last edited: Mar 24, 2011
15. Mar 24, 2011

### CosmicVoyager

Okay, this sounds promising :-) So you are saying there *is* a way of reconciling the apparent contradictions. Could you or anyone explain the idea in detail like ghwellsjr did with his scenario, preferably with illustrations (but anything is welcome)? ghwellsjr's explanation almost worked. I am imagining the 2d to 3d equivalent of this 3d to 4d scenario, and I don't see how one's speed would cause one to see a higher dimensional object from a different angle. My speed would not cause the object to rotate, and my speed would not move me up or down off my plane. Thanks.

*edit
I thought about this some more and realize that everything including the observer would be 4-dimensional objects. If that were true, why do we only see and move in three? Why are we confined to 3 axes?

Last edited: Mar 24, 2011
16. Mar 24, 2011

### ghwellsjr

If my "explanation almost worked", I'd like to know where it disappointed you. What are the "apparent contradictions" that you would like reconciled?

17. Mar 24, 2011

### Rap

Draw a graph, vertical axis is time in years, horizontal axis is space in light years. That's "your" space and time. That means that a light beam will be at a 45 degree angle. Now draw a line from the origin upwards and to the right, at an angle to the vertical (time) axis that is smaller than 45 degrees, so it represents a person moving slower than the speed of light. The old, classical way of looking at things (i.e. "Galilean") says that the time axis for that other person is the vertical axis and the space axis for that other person is the horizontal axis - same as it is for you. Einstein said, no, the time axis for that moving person is the slanted line, not the vertical line any more, and the space axis for that person is perpendicular to that time axis, not the horizontal axis any more. Thats how the rotation happens. There is no special space or time axis, everybody makes their own.

Draw two dots on the graph. These are events, like firecrackers going off, they have a fixed point in spacetime. You drop a perpendicular from those points to your space axis - that's the distance you see between the events. You draw a perpendicular to your time axis - that's the time you see between these events. Draw a perpendicular to the other person's space and time axes, that's the space and time intervals that they see between these events - totally different.

Now comes the hard part - spacetime is not a Euclidean space. The distance between two points in Euclidean space is the square root of x^2+y^2+z^2 no matter what your axes are, but in spacetime, the spacetime distance between two points is the square root of x^2+y^2+z^2-t^2 (x,y,z in light years, t in years) no matter what your axes are. That minus sign in front of t^2 changes things. It means that what you draw as perpendicular on your Euclidean graph paper does not represent a perpendicular in non-Euclidean spacetime. For your space and time, the perpendiculars you draw on your graph are ok, but a perpendicular to the other person's time axis does not drop below your space axis at the same angle, it goes above it by the same angle, and when you draw perpendiculars to the other persons space and time axes, they won't look perpendicular on your Euclidean piece of paper. As the other person goes faster and faster, their time axis will get closer and closer to the 45 degree line, the speed of light, and their space axis will get closer and closer to that 45 degree line as well. If you tell the other person to draw a graph of things, like you have done, they will say that the speed of light is 45 degrees on their graph too! This gives you a feel for why the speed of light is special.

Last edited: Mar 24, 2011
18. Mar 24, 2011

### CosmicVoyager

As I said above,
"If I were to measure out the distances between my mirrors when I am stationary to you, and I and all of the mirrors were to accelerate together, then they should still be arranged in a circle because as the mirrors narrow, the space between them increases since they are not connected."

To which you replied,
"You are correct when you say if the mirrors accelerate together, you mean that you put individual rockets on each mirror and accelerate each of them with no rigid connectors between them but if you mean they are fastened to some kind of structure and you have only one rocket that accelerates the entire structure together, then the mirrors will move closer together."

If I measured them out into a circle, then accelerated and they remained in a circle then they are not in the ellipse needed to make the light appear to travel at the same speed for me as it does for you.

Anyway, Janus replied saying,
"Length contraction is not something that "physically" acts on objects. It means that reference frames in motion with respect to each other measure the length differently. In other words, if there are two points in space that are 1 meter apart according to you, for someone traveling parallel to the line joining them, these two points will be closer together, regardless of the fact that there is no physical connection between those points or even if there is any physical objects at those point.

So in your above examples, the distances between the discreet objects also length contract."

To which I replied,
"Okay, this is what I was afraid of. It seems to me this "length contraction" idea is just a convenient mathematical correction to compensate for something we have no explanation for, made up so that things will work out in calculations so that it can be predicted how things will *appear* in different circumstances. It is not really happening. Rulers are not contracting. And space is certainly not expanding and contracting based on how fast an object is moving. So it is extremely misleading to say objects flatten the faster they go. The correct answer for how it is that the speed of light can be measured to be the same regardless of one's speed is "No one knows. We only know how to calculate what the results of measurements will be."

Last edited: Mar 24, 2011
19. Mar 24, 2011

### CosmicVoyager

I do not follow this explanation :-(

I was expecting an explanations using four physical dimensions with 4d objects like hypercubes.

I do not see how to translate it into a specific such as the one in my first post or the one ghwellsjr gave. I am wondering if this can be illustrated with the universe as a plane with 2d objects on it and other planes being time.

This just seems to be a graph of how things appear, and not an explanation for how it is that they can appear hat way, not how observers moving at different speeds could measure something (light) to be the same speed like ghwellsjr animation was.

"spacetime is not a Euclidean space. The distance between two points in Euclidean space is the square root of x^2+y^2+z^2 no matter what your axes are, but in spacetime, the spacetime distance between two points is the square root of x^2+y^2+z^2-t^2 (x,y,z in light years, t in years) no matter what your axes are."

So it really isn't distance. Time is not a physical dimension. Time is concept. I line representing time is a graph of changes in the arrangement of objects. And if you were to add a fourth axis it should add the same distance as adding a second and third do.

Also, if time were a fourth dimension that the universe was in then there are two possibilities, both of in which the above explanation does not work:

Possibility A - Everything in the universe is moving through time. The past and the future are empty. Objects could not be at a different place in time than other objects because they would disappear from the slice of time that the rest of the universe is in.

Possibility B - Objects are four dimensional and extend backward in time. They are *extremely*, if not infinitely, long and connect to each other in the past. If this were the case then we should experience all of time at the same time and not just one slice of it, since we are four dimensional objects that are everywhere in time.

20. Mar 24, 2011

### Rap

No - it IS a distance. Time IS a physical dimension. Its just that the 4-dimensional space in which things exist (spacetime) is not Euclidean. The geometry of things on the surface of a sphere is not Euclidean: the sum of the angles of a triangle on the surface of a sphere do not add up to 180 degrees. The distances in spacetime are not all positive real numbers. So what?

There is no unique "slice of time" that the universe is in. This is the whole point - the world is four dimensional, objects are four dimensional, and different people make different slices. Your slice is yours, mine is mine. I make a "slice of time" and the universe looks a particular way. You make a different slice, it looks different. Its the same four-dimensional universe, but different slices. Some things that I call "now", you might call "later". A ruler is a four dimensional object. How long is it? One person takes a slice of the 4-D ruler and gets an answer. Another person takes a different slice, gets a different answer. It makes no sense to ask "how long is the ruler?". You have to ask "by whose slice?". This is what the Lorentz contraction is all about.

But our consciousness does not experience things that way. Our consciousness experiences successive slices of the 4-D universe. If you ask why, then that is a real problem, I don't think anyone knows the answer to that. In that sense, relativity is using equations that tell us what we experience without knowing why. But its not just a bunch of equations, or, if they are, its amazing that they describe a four dimensional space in every bit of detail as the equations we use for our 3-dimensional space, geometry, physics, topology, everything. Searching for a true paradox in the geometry of spacetime is like searching for a paradox in Euclidean geometry. Very, very difficult. All paradoxes boil down to not understanding the geometry of spacetime. All contradictions are indeed apparent, as long as they are based on measurements.

Last edited: Mar 24, 2011