TimeTopics

Different perspectives of timeSimultaneityWhat is “now”?The arrow of time

MotivationTrying to understand this most slippery of concepts.

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Special relativity Motion through time and motion through space, are linked. High relative velocities produce Lorentz time dilation.

General relativity Spacetime can be warped. Massive objects can produce gravitational time dilation.

Time is not a uniform metric that is equable to all observers.

Let us remind ourselves about how special relativity smashed the concept of simultaneity….

Einstein and time

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Events are “simultaneous” if they happen at the same instant in time. We see them happen simultaneously because the light pulses reach us at the same time.

The finite velocity of light complicates the issue slightly, because light from objects further away must travel further (i.e., longer). However, we can account for this effect.

Simultaneity

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What is now? Events around the Universe that happen at the same time share the same now.

We can make a list of everything that is occurring now.

—We are in class now. (t=0)

—A lunar probe sends a signal now. (t=1.28 s)

—Radiation is leaving the Sun’s surface now. (t=500 s)

—Two comets in the Oort cloud collide now. (105 au, t=579 d)

—A star in the Andromeda galaxy ignites He now. (t=2.5×106 y)

—A star explodes in a distant galaxy now. (5 GLY, t = 5×109 y)

—A star explodes in a galaxy on the other side of the observable universe now. (47×109 LY away, t >> 47×109 y)

Time and the now

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Recall from relativity

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L

The trainside observer sees two lightning strikes share a now.

But the train passenger observes that the two strikes do not share a now.

We see that motion modifies whether or not events share a now.

Shift your frame to one moving, relatively, to the right...

The two stars at the right popped earlier than the star on the left.

Relativity and the now

t=t1 t=t2

This is important enough, let us repeat it.

What does the observer see?

The events are not simultaneous. They are not in the same now.

Remember: you cannot say that the loss of simultaneity is because the observer is moving. Who is to say who is moving, in empty space?

Relativity and the now

How much of an effect is this?

Suppose an event far away (at distance L) happens now (adjusted for light travel time). If you shift to a reference frame moving (at a velocity v) towards the event, you shift it out of that now, by a time interval (∆t):

Approach it, and it happened earlier (at a more ancient now).

Move away from it, and it happened later (at a more futuristic now).

Relativity and the now

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L

Bring back some of the events on our now-list.

If you move at 2.5 m/s (jogging speed)

If you move at 885 km/hr (speed of a commercial jet)

—Radiation left the Sun’s surface...

∆t = 4×10-6 s earlier than now

—Two comets in the Oort cloud collided...

∆t = 0.4 s earlier than now

—A star in the Andromeda galaxy ignited He...

∆t = 7.6 d earlier than now

—A star exploded in a 5 GLY galaxy…

∆t = 42 y earlier than now

—A star exploded on the other side of the observable universe…

∆t = 390 y earlier than now

How much does velocity shift now?

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∆t = 0.4 ms earlier than now

∆t = 40 s earlier than now

∆t = 2.0 y earlier than now

∆t = 4100 y earlier than now

∆t = 38000 y earlier than now

Reverse the roles….

If someone is moving away from us, they would include parts of our past in their own now list.

If they change their direction and move towards us, they would include parts of our future in their own now list.

What part of your now?

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Think of everything in the now as a frozen instant in time.

As one now transitions to the next, and the next, and the next, it is like different frames in a film.

Interestingly, there is nothing in the laws of physics that embodies this notion—of a slice of reality that is illuminated, one now after another.

Even our innate sense of time flow (that now flows from one moment to the next) is not supported by physics.

Furthermore, there is nothing in physics that says we should be at any specific point in our timeline.

Now and physics

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As one now transitions to the next, it is like looking at a loaf of bread, one slice at a time.

The effect of motion is to change the events of now—it changes the angle at which you cut the bread.

The faster the speed, the more angled the cut.

Depending upon your speed, all of time, every event in the history of the universe, can be made to be happening now.

Is there even any sense to the concept of now?

Now and a loaf of bread

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Let us examine why time seems to move in one direction.

Why can’t we remember the future?

Why can’t we change our pasts?

This one-directionality is called the “arrow of time.”

Why does time have a direction?

Time’s arrow

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A ball fired upwards at an angle, in a vacuum, travels in a parabolic trajectory.

Film the ball in its trajectory, show it in reverse, and it would look exactly the same!

This symmetry indicates that physical laws are symmetric in time.

Indeed, all laws in physics are symmetric in time. Film something happening, and it can be shown in reverse, with no violation of physical laws.

Time

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Can you even run explosions in reverse?

Yes! Even though it might be seem contrived, it is entirely possible to rig an explosion in reverse (an implosion), so that you fire a whole set of fragments together, to assemble a bomb, in reverse.

While possible, there is no denying that this would be difficult.

The example of the bouncing ball is similarly asymmetric on close inspection. Friction with air makes it slower in the way down.

You could conceivably recreate the bouncing ball in reverse by bombarding the ball with carefully aimed molecules, so it would rise slowly, and then fall more rapidly on the final part of its bounce.

Explosions?

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The Universe ages in one direction because there is an overwhelming tendency for things to become more disordered.

It appears that time—whatever it actually is—is closely associated with randomness in nature (entropy).

The flow of time IS the same as the drive for systems to become more disordered.

Our Universe began in a highly ordered state—uniform, unclumpy energy and matter confined by a strong gravitational field. The story of the big bang is the story of a Universe becoming messy.

The expansion of the Universe into larger scales began the flow of time.

The arrow of time

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I wonder. Does time have meaning in empty space? Does time proceed only because the Big Bang happened?

And what about a piece of “empty space” in our Universe. Does time proceed in it? Perhaps, because empty space is curved and expanding?

Ruminations

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