### Video Transcript

The principle of conservation of
energy states: the amount of energy before an energy conversion is equal to the
amount of energy after the conversion. There have been some examples where
a scientist has claimed to have found an energy conversion process in which more
energy existed after the conversion than before. A scientist does experiments where
they measure a small energy increase after a conversion process. Suggest why the scientist might not
want to share their experimental results publicly.

We see here what the principle of
energy conservation states. And we also see that in the history
of science, there have been some examples where this principle seems to have been
violated. Nonetheless, the principle
continues to stand and in fact is one of the better supported notions in
science.

With that as background, we come to
our particular question which is a scientist has done a set of experiments, in which
it does seem that this principle is violated — that more energy came out of a
process than went into it. We want to make a suggestion as to
why the scientists might not be enthusiastic about sharing these results
publicly.

The reason for this goes back to
what we were saying about this principle of energy conservation being so well
established. We can use an analogy to this
particular instance to help explain. Imagine that we’re working on a
laboratory exercise. And in this exercise, we’re
studying circuits.

In particular, by making
measurements of the various components of this circuit, we want to verify Ohm’s law,
which says that 𝑉, the potential difference, is equal to the current in the circuit
multiplied by the total resistance.

Let’s imagine that we’re given the
potential difference 𝑉 and we measure 𝑅 one, 𝑅 two, and 𝑅 three, the three
resistors in the circuit. And then we’ve our ammeter placed
in series, we measure the current running through this loop. With all these values calculated,
say we combine them then to see if they confirm Ohm’s law. And say that even allowing for
experimental uncertainty, they don’t; that is, they seem to contradict Ohm’s
law.

If this happened to us in a
laboratory exercise scenario, there are a few different conclusions we could
draw. One conclusion is that our result
is correct and Ohm’s law, one of the best supported and most thoroughly tested laws
in physics, is actually incorrect. We could also conclude that our
result as well as Ohm’s law are both incorrect or — and this is perhaps more likely
— we might look with suspicion on the numbers that we measure in the calculation we
went through.

After all, if it doesn’t agree with
such a carefully evaluated law, might there be something incorrect about what we’ve
done. This gets to the heart of this
question of why the scientists doing an energy conservation experiment might not
want to present those results at first.

We could say that the scientists
might well think that it was quite possible that results that disagree with a
well-known theory would contain errors and so would not want to present them. It’s possible of course that the
scientist’s process and conclusions were all correct and that it’s the theory that
needs to be adjusted.

But again, when a theory is so well
tested as this one is, the more likely explanation is that an error has been made in
the experiment. If you were in the scientist’s
situation, what would you do? Let’s continue on and see what
happens.

The scientist repeats the
experiments and continues to find a small energy increase after each conversion. The scientist has no explanation
for how the energy increases happen and cannot find any errors in their
measurements. The scientist decides to share the
results publicly to see if any other scientists know of any theories that can
explain the energy increases. Suggest two other reasons why the
scientist might publicly share the results.

So the plot has thickened. The experiment has been redone. But instead of resolving the
question, it just deepens the question. What’s going on? Many of us have been in the same
situation. No matter how carefully we walk
through an experiment, our results simply do not agree with what we expect.

So now, the scientist decides it’s
time to share news of this experiment with the scientific community to see if anyone
else can explain just why the energy is increasing through this process. What we want to do is suggest two
other reasons why the scientist might have an incentive to share the results. Let’s think through what would
likely happen if news of this experimental result comes out publicly.

One thing that will probably happen
is that other scientists will try to reproduce these results. That is, they’ll try to run the
same exact experiment and see if they find the same thing. If and when they do that, a couple
different outcomes could occur; both of which will be helpful for addressing this
overall question.

In the first case, they might run
the same experiment and indeed find results that seem to violate the principle of
energy conservation; that is, the results would support what the scientist has
found. So that’s one reason to share the
results publicly in order to see if any other scientists can get experimental
results that also do not conserve energy.

And another possible outcome is
that when these other scientists redo the original experiment, they themselves might
detect an error or errors in the process. In other words, they’re reviewing
or double-checking the work of the first scientist. This then is a second reason to
share these results publicly to see if anyone else can spot errors in the original
process.

At this point, it’s more helpful to
discover any errors that might be there than to go on being confused about why the
results don’t seem to agree with a well-established principle. We see then that there is a time
for double-checking our work before going public with it and that there’s a time of
asking for input from others in order to spot any errors we might have made or to
confirm our results.

Next, let’s start working with some
of the numbers involved in this experiment.

A hypothesis is suggested to the
scientist. According to the hypothesis, the
input power to the energy conversion is predicted to be 1.00065 gigawatts and the
output power from it is predicted to be 1.00068 gigawatts. How many watts is equal to 1.0006
gigawatts? Give your answer in standard
form.

One thing we can notice about this
question is that it refers to a number, which is different from either the input or
output values given to us in this background statement. So we just want to be careful not
to confuse these values we want then to convert this value, 1.0006 gigawatts, into
units of watts.

To start on our solution, let’s
consider this prefix giga and what it means for the number we’ve been given. In general, the prefix giga refers
to one billion, 10 to the ninth of whatever quantity is being considered. When we’re talking about watts then
like in this case, we can say that one gigawatt is equal to 10 to the ninth or one
billion watts.

And let’s now apply this
relationship to our actual given number, 1.0006 gigawatts. This number of gigawatts must equal
that same number times 10 to the ninth watts. This is the number of watts written
in standard form equal to 1.0006 gigawatts.

Let’s continue on with another
calculation related to this experiment.

The energy conversion is measured
by the scientist to last for 1.25 nanoseconds, using timing apparatus that has a
resolution of 0.01 nanoseconds. How many more joules of energy
output than energy input does the hypothesis predict would be produced in 1.25
nanoseconds?

To go about answering this
question, let’s recall what the hypothesis predicted. What the hypothesis let us to
expect is 1.00065 gigawatts of power input to the process and 1.00068 gigawatts
output.

We notice that according to these
numbers there is more power output than input. And that’s the source of our
confusion about this result. For the purposes of this question
though, we’ll leave that aside and we’ll simply consider how many more joules of
energy output than energy input does this hypothesis predict.

We can start off by comparing the
output power to the input power. And like we said, the output is
actually greater than the input. We can call the change in power
that occurs over the 1.25 nanoseconds in the energy conversion to be Δ𝑃.

Δ𝑃 is equal to the output power
1.00068 gigawatts minus the input power 1.00065 gigawatts. When we perform this subtraction,
we get the very small seeming number of 0.00003 gigawatts. But remember giga is a prefix
indicating billion. And when we recall this conversion
and apply it to this particular number, we see we’re actually working with the
number of three times 10 to the fourth or 30000 watts.

By calculating Δ𝑃, we’ve now
calculated how many more watts of power output than power input occurred in this
process according to the hypothesis. But our question doesn’t ask for
watts of power, but rather joules of energy. So we want to convert between these
two units.

To do that, here’s what we can
recall: a watt which is the unit of power is defined as a number of joules of energy
divided by a time in seconds. We can apply this definition of
watt to our result Δ𝑃. This amount of power is equal to
the total number of joules of energy converted in the process divided by the time
the process took. And in fact, we’re told what this
time is in the question statement. It’s 1.25 nanoseconds.

The prefix nano is like the
opposite of the prefix giga. Whereas giga means billion, nano
means one billionth, which means that 1.25 nanoseconds is equal to 1.25 times 10 to
the negative ninth seconds. And looking at this resulting
equation, we see it involves what we want to solve for: the joules of energy
converted as well as known values.

Rearranging this equation, we see
that the number of joules output greater than the number of joules of energy input
is equal to three times 10 to the fourth watts multiplied by 1.25 times 10 to the
negative ninth seconds. This results in a value of 3.75
times 10 to the negative fifth joules. This — so it seems from our
experimental results — is the amount of energy that’s created, seemingly out of
nowhere, through this experimental process.

For our next step, let’s consider
the precision of one of the numbers involved in these calculations.

The power input and output values
used in the hypothesis have a precision of six significant figures. To how many significant figures a
precision is the measurement of the time during which the energy conversion
occurs?

Let’s recall what that time
was. The time for this conversion
process was given as 1.25 nanoseconds using a process that had a resolution of 0.01
nanoseconds. That resolution tells us that all
three of these figures are significant. When we write out this time value
in standard form, we see that the coefficient — also called the significant —
confirms this.

All three of the digits — one and
two and five — are significant in this time. Our answer to this question then is
three significant figures. That’s the precision to which the
time is measured during this energy conversion process.

Lastly, as we consider this
experimental process, let’s take a step back and think of any assumptions we might
have made.

The input power and output power
cannot be properly tested with the experimental instruments that the scientist
uses. What assumption does the hypothesis
make to conclude that the energy is not conserved?

Recalling that hypothesis from
earlier, we recall that it told us that the output power minus the input power is
equal to a positive value 30000 watts. This number would have to be zero
for energy to be conserved in this process according to the hypothesis. Since it’s not and since it’s a
positive value, it tells us that this process is hypothesized to create energy out
of nothing.

That’s where this agreement with
the energy conservation principle comes in and that’s what this whole discussion is
about. But like any hypothesis we might
make about experimental results, there are certain assumptions involving this
one. Here is one way to picture our
understanding of this experimental process.

Our understanding is that some
amount of energy goes in to our experimental process or setup or method and then
some amount of energy comes out. When we compare the energy out to
the energy in, we expect those to be equal to one another. After all, that would agree with
the principle of energy conservation.

But notice something we’re
assuming. We’re assuming there’s only one
energy input source and only one energy output; that is, that there’s a single
overall process going on by which energy is taken in and energy is output and that
it’s those inputs and outputs we’re comparing. That’s an assumption we’re making
because as a matter of fact there could be more than one energy input source and
more than one energy output.

If this was the case, then simply
comparing one energy input source with one energy output source wouldn’t be a good
test of the principle of energy conservation. Instead, we would need to consider
all the energy inputs and all the energy output across however many processes we’re
going on in this experiment.

When we claim through our
hypothesis that there is only one energy input source and one energy output source,
that’s an assumption we’re making which might not be correct. Moreover, not only could there be
multiple processes going on, but remember that we’re looking at energy conservation,
whereas our hypothesis speaks to power.

Power unlike energy involves the
element of time. And we’ve made an assumption when
we talked about the process taking 1.25 nanoseconds that the energy input and the
energy output processes were taking the same amount of time.

Let’s put all this into words about
what assumptions this hypothesis makes. We can write that the hypothesis
assumes that the input power to the process continues for the same amount of time
that the output power from the process continues.

In other words, the input and
output are all part of the same process, which takes the same amount of time. That’s an assumption we’re making
and it might not be accurate. Indeed, it may point to the source
of our disagreement with the principle of energy conservation.