A Simple Demonstration of Space/Time Relativity

[snowtracks]

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This is so simple, I’m sure others have thought of it. So, it’s only relatively original.  All you need is a piece of paper, some scissors, and a pen or pencil.

1. Cut the paper into a perfect circle. You can do this easily by folding the paper and cutting it in half a circle.
2. Find the exact center of the circle and place a dot there.
3. Two inches from the center place another dot.
4. In line with the first two dots, place another dot four inches from the center.
Distances don’t matter, but to make things simple and ease your observation, keep your dots in one line along one radius from the center to the circumference of your circle.

Now rotate your circle using the center dot as your axis. Note, this is one solid piece of paper so it’s all moving at the same speed. Yet while the center dot stays in place, the second dot my move an inch and the third dot may move two inches.

How can this be? how can objects moving at the same speed, for the same duration of time, move different distances?

Once you  grasp the basic concept you can experiment with different distances using triangulation and epicurean mathematics to make calculations and satisfy your own curiosity.

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Special Relativity states equivalency: The faster through space, slower in time.

[BryanS]

And is there no connection between radial speed and time dilation?

Not in particular, no. Only if the magnitude of its linear velocity approaches a value that is large relative to the speed of light (3.0 x 10^8 m/s).

magnitude of linear velocity = angular speed (measured in radians/s) times radial distance from center of rotation
v = w * r

Two objects with the same angular speed can have vastly different magnitudes of linear speed. Think of being on a merry-go-round on a playground. If you position yourself just off of center, you are not moving very fast, but if you position yourself near the edge, you are moving faster in space. Two objects on the same spinning merry-go-round at different radial locations will have different speeds. 

The principle of special relativity would tell you that a merr-go-round that is spinning such that its outer edge is moving at speeds near the speed of light will see the outer edge time passing slower than another location near the center. But that has to do with the difference in linear speed, not in particular how fast it is rotating. It would be possible for two spinning objects with the same angular speed but different sizes to result in the larger object experiencing relativistic effects while the smaller one does not. It all depends on how big radial distance "r"  is.

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I should add that when you discuss "space time" relativity, you are referencing Einstein's special relativity, which is a lot more complicated than your apparent understanding of the concept. Special relativity relies on two assumptions:
1. The laws of Physics do not change based on space and time frame of reference.
2. The speed of light is always constant regardless of your space and time frame of reference.

You appear to be incorporating some understandings of Newtonian relativity. This is the sort of relativity that says if you are moving in a car that goes 10m/s and throw a ball ahead of the car at 5m/s, the ball appears to a person on the ground to be moving 15m/s.

Einstein proposed that for light, a person in a car moving 10m/s shining a flashlight sees light moving at 3.0x10^8 m/s. The person on the ground sees the exact same speed of this light being 3.0x10^8 m/s, which would violate Newton's understanding of relative motion. Everything else in relativistic physics, including that E=mc^2 equation many associate with Einstein, is derived with just the two above assumptions. But to see any relativistic effect at all, the number sqrt( 1 - v^2/c^2) has to be significantly less than 1. So no, a human is not capable of physically rotate a piece of paper and achieve anything close to the speeds necessary to observe special relativity. I somewhat doubt humans have created a mechanical device that could even do that.

[Rhondazvous]

And is there no connection between radial speed and time dilation?

Not in particular, no. Only if the magnitude of its linear velocity approaches a value that is large relative to the speed of light (3.0 x 10^8 m/s).

magnitude of linear velocity = angular speed (measured in radians/s) times radial distance from center of rotation
v = w * r

Two objects with the same angular speed can have vastly different magnitudes of linear speed. Think of being on a merry-go-round on a playground. If you position yourself just off of center, you are not moving very fast, but if you position yourself near the edge, you are moving faster in space. Two objects on the same spinning merry-go-round at different radial locations will have different speeds. 

The principle of special relativity would tell you that a merr-go-round that is spinning such that its outer edge is moving at speeds near the speed of light will see the outer edge time passing slower than another location near the center. But that has to do with the difference in linear speed, not in particular how fast it is rotating. It would be possible for two spinning objects with the same angular speed but different sizes to result in the larger object experiencing relativistic effects while the smaller one does not. It all depends on how big radial distance "r"  is.

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I should add that when you discuss "space time" relativity, you are referencing Einstein's special relativity, which is a lot more complicated than your apparent understanding of the concept. Special relativity relies on two assumptions:
1. The laws of Physics do not change based on space and time frame of reference.
2. The speed of light is always constant regardless of your space and time frame of reference.

You appear to be incorporating some understandings of Newtonian relativity. This is the sort of relativity that says if you are moving in a car that goes 10m/s and throw a ball ahead of the car at 5m/s, the ball appears to a person on the ground to be moving 15m/s.

Einstein proposed that for light, a person in a car moving 10m/s shining a flashlight sees light moving at 3.0x10^8 m/s. The person on the ground sees the exact same speed of this light being 3.0x10^8 m/s, which would violate Newton's understanding of relative motion. Everything else in relativistic physics, including that E=mc^2 equation many associate with Einstein, is derived with just the two above assumptions. But to see any relativistic effect at all, the number sqrt( 1 - v^2/c^2) has to be significantly less than 1. So no, a human is not capable of physically rotate a piece of paper and achieve anything close to the speeds necessary to observe special relativity. I somewhat doubt humans have created a mechanical device that could even do that.

V = w * r. well, I guess that would be closer to Newton than Einstein since it involves dots on a piece of paper rather than light. Although light does behave the same way. If you swing a flashlight from side to side the light farthest from you will travel a farther distance than the light near you although it seems to be going the same speed.

Certainly, if Einstein’s special relativity theory isn’t more complex than my understanding of it, then it should be taught in grammar school. I don’t claim to be more than a student who’s not afraid to put my ideas out there to sink or swim as they may.

I don’t know if Einstein relativity violates Newtonian relativity or if it simply demonstrates the different properties of light (a boson) and a ball (fermions).

That the light moves with the flashlight when it is moved sideways but not when it’s moved forward is curious. But the flashlight itself does follow Newton.

[BryanS]

V = w * r. well, I guess that would be closer to Newton than Einstein since it involves dots on a piece of paper rather than light. Although light does behave the same way. If you swing a flashlight from side to side the light farthest from you will travel  a farther distance than the light near you although it seems to be going the same speed.

Certainly, if Einstein’s special relativity theory isn’t more complex than my understanding of it, then it should be taught in grammar school. I don’t claim to be more than a student who’s not afraid to put my ideas out there to sink or swim as they may.

I don’t know if Einstein relativity violates Newtonian relativity or if it simply demonstrates the different properties of light (a boson) and a ball (fermions).

That the light moves with the flashlight when it is moved sideways but not when it’s moved forward is curious. But the flashlight itself does follow Newton.

It's not quite that Einstein's special relativity violates Newtonian relativity. But rather Newtonian relativity is a special case of Einstein's relativity. All of the laws of mechanics laid out by Newton are derived in special relativity with the two assumptions I specified. The equations are mathematically inaccessible to grade schoolers, so that is why you will not see this taught to people that young. When equations for special relativity are utilized for slow speeds relative to the speed of light, they approach the exact same form of Newtonian equations. 

Special relativity is not some special property of light. But rather in formulating equations based on the assumptions of special relativity, the speed of light becomes a built in speed limit for all objects regardless of their mass. E=mc^2 is the energy derivable from special relativity for an object with mass that is at rest--the relationship between energy and mass is a direct consequence of the theory of special relativity. This relationship between mass and energy comes from a universal relative speed limit. Special relativity has little to say about bosons and fermions, which by their definitions describe a quantum property that special relativity has nothing to say on. To date, there has been no successful merging of quantum theory with relativity. Perhaps one day we will find some relevance of special relativity to quantum theory, but that day is not today.

Your example of swinging a flashlight misses the mark somewhat. Light does not "move with the flashlight". Photons emitted from the light element in the flashlight always move at exactly the same speed regardless of what you are doing with the flashlight, regardless of which way the flashlight moves, and regardless of how fast the flashlight moves.

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One other thing to add...electrons are examples of fermions with mass, and these are something we can accelerate to relativistic speeds. Relativity applies to all objects, not just light.

[Vince]

As others have said when things are spinning the speed is measured in radians/sec not a distance per second.  So all points on the disk have the same radial speed.  As the points go further out from the center they have to travel a longer distance to keep up but they are still going the same radians/second (radial speed) as every other point.

And is there no connection between radial speed and time dilation?

sure. There is a time dilation between any objects moving at different velocities. However at slow speeds the dilation is so small it is not noticed. Time on the ISS is lagging behind the earths about 0.007 seconds every year I think.