Touch a Star

You can touch a star. For real. And you won’t get burned. Disclaimer: I’ll need to stretch the definition of “touch,” but the laws of physics support my interpretation. You’ll need to flex your brain a bit, and engage some philosophy, but if you stay with me, I promise you a remarkable insight.

What started me down this line of thought was a quote from Gilbert Newton Lewis (1875-1946), an American chemist whose work advanced the science of thermodynamics during the early part of the last century:

“Any pair of points [in spacetime] which are separated by zero distance are in virtual contact.
In other words, I may say that my eye touches a star, not in the same sense as when I say that
my hand touches a pen, but in an equally physical sense.”

— G.N. Lewis, “Light Waves and Light Corpuscles”, Nature Feb 1926

What was Lewis saying? In this post, I’ll try to put some context around that quote. The following section provides some scientific background. It draws on the laws of special relativity (SR). If you need to review that paradigm-changing theory, just follow this link to a nicely done website called Einstein Online.

First the physics:

The graphic above shows three scenarios charting the distance between a spacecraft at Earth and the bright star Alpha Centauri (α Cen), located 4.4 light years (LY) distant. Earth is the green object, α Cen is the yellow object, all the other objects are random stars in space.

Only the X and Y axes are shown to define this volume of space. There is a Z axis that extends perpendicular to X and Y, into and out of your screen, but it is omitted for simplicity.

In the left panel, the spacecraft and α Cen are at rest with respect to each other. In the middle panel, the spacecraft is moving with v = 0.87c (87% the speed of light). In the right panel, the spacecraft is moving with v = c (the speed of light) = 300,000 km/s = 186,000 miles/s.

Now according to SR, and as experimentally confirmed, space will contract in the direction of motion (in this case the Y axis) by the Lorentz Factor γ (gamma) where:

γ = 1/(1-v2/c2)0.5

So when moving with v = 0.87c, γ = 2.0 and the spacecraft experiences all of space contracted by 50% in the direction of its motion. Observers on the spacecraft measure the distance to α Cen not as 4.4 LY, but as only 2.2 LY. All the stars ahead would appear blue-shifted. Earth and α Cen (kept at their original colors) would be contracted into ellipsoids, as would the stars. Behind the spacecraft (not shown) the stars would appear red-shifted.

When moving with v = c, space would be contracted by 100% and the distance to α Cen would be zero. The X-axis is reduced to a point, and 3D space is now a 2D plane defined by the Y and Z axes.

Note: Spacecraft cannot move at the speed of light. This is a gedanken experiment. We are simply asking the laws of physics “What would happen if?” And the laws of physics tell us: if v = c then γ = Δd = 0.

Next the kinematics:

Now just for kicks, let’s calculate some travel times for this hypothetical voyage. At a speed of 0.87c (physically possible but very energy-intensive and expensive), an observer on Earth could measure and verify the spacecraft’s speed v = 0.87c. Since the distance to α Cen is 4.4 LY, the travel time would be:

1. ΔT = Δd / v = 4.4 LY / 0.87c = 5.06 years.

But on the moving spacecraft, where space is contracted, the distance to α Cen is only 2.2 LY. Thus:

2. ΔT = Δd / v = 2.2 LY / 0.87c = 2.53 years.

That’s only half the time Earth measures for the voyage! It would “seem” the spacecraft must be moving at twice the speed of light — clearly an impossibility. This apparent violation of the laws of physics will be explained shortly.

But first, let’s do one more calculation. Say the spacecraft was moving with v = 0.999c (99.9% the speed of light). In that case, the Lorentz factor would be γ = 22.37, and space would be contracted in the direction of motion to 0.045 of its at-rest length. The distance to α Cen is now a mere 0.20 LY, as measured by the moving spacecraft. From Earth, at rest, the distance remains its original 4.4 LY. Thus:

3. ΔT = Δd / v = 4.4 LY / 0.999c = 4.404 years (as measured from Earth), and
4. ΔT = Δd / v = 0.20 LY / 0.999c = 0.2002 years = 2.5 months (as measured in the spacecraft).

I think you can see where this is going. By incrementally increasing your speed closer and closer to the speed of light, you can reduce the travel time to whatever you need. Less than an astronaut’s lifetime, for example, if an expeditionary round-trip is what you want to do.

You’re probably wondering at this point, which travel time is “correct” — is it 4.404 years or 2.5 months? The short and unintuitive answer is: Both. Observers on Earth would measure the clocks on the spacecraft as ticking more slowly by the same Lorentz factor of γ = 22.37, so they would calculate the spacecraft’s journey to α Cen took a time of:

5. ΔT = γ × 0.2002 years = 22.37 × 0.2002 years = 4.404 years (the same result as in calculation 3).

From Earth’s point of view, time slowed down on the spacecraft. From the spacecraft’s point of view, the distance to α Cen contracted. But both observers would agree on the speed of light, and measure their relative speeds as equal and opposite.

The slowing of time on moving objects is an SR effect known as time dilation. It has also been experimentally confirmed. These calculations show how both space and time are altered by motion. The speed of light is measured as v = c by all observers, regardless of their motion. Einstein’s insight was realizing this experimentally verified fact required space and time to be flexible.

Now the philosophy:

Ask yourself the question: What would the Universe look like if I were a photon of light? This is another gedanken experiment, of course. It’s the question Einstein pondered, and it ultimately led to his insights about space and time.

The answer is counter-intuitive: For a photon of light leaving any star and heading toward Earth, the distance it must travel is zero, and the time it takes (if that even means anything to a photon) is also zero. The photon is created by an electronic transition in an atom on that star. It instantly takes off at the speed of light, heading for an atom in the retina of the eye looking at that star. There the photon is absorbed by an atom in a rod or cone and converted into an electrical impulse that allows your brain to perceive that star. But for that photon, this all happens simultaneously.

There’s a another famous quote, often attributed to Woody Allen: Time is just Nature’s way of keeping everything from happening at once. Clever, for a non-physicist. In fact, for a photon of light, everything does happen at once.

So for that photon we were talking about, it is touching the star of its origin, and at the same “time,” it is touching your eye. If I may now invoke the symmetric property of equality from logic (if A=B then B=A), I can conclude that your eye is also touching that star.

In a very real sense, you are involved in a cause-and-effect chain that connects you intimately to an object far off in space. But it is as here-and-now as your hand touching the hand of a loved one. I think this is what Lewis was saying. So go outside tonite, find a bright star, and touch it. The photons will be there any time, awaiting first contact.

Next Week in Sky Lights ⇒ Harvest Moon on September 9

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Harvest Moon on September 9